A class of generalized decision- feedback equalizers

An upper bound and a lower bound to the probability of error for data transmission systems using a decision-feedback equalizer, with error propagation effects taken into account, are presented. Numerical examples show that they are tight bounds.We introduce the concept of a generalized decision-feedback equalizer suggested by the form of the derived bounds. A subclass is studied and optimized numerically with the aid of the derived error probability bounds. The solution represents the best compromise achievable by that class between the output noise power and the output intersymbol interference due to error propagation. A numerical example is carried out in detail to illustrate the concept.     

Recursive state estimation based-on the outputs of partial nodes for discrete-time stochastic complex networks with switched topology

In this paper, the state estimation problem is studied for a class of discrete-time stochastic complex networks with switched topology. In the network under consideration, we assume that measurement outputs can be got from only partial nodes, besides, the switching rule of this network is characterized by a sequence of Bernoulli random variables. The aim of the presented estimation problem is to develop a recursive estimator based on the framework of extended Kalman filter (EKF), such that the upper bound for the filtering error convariance is optimized. In order to address the nonlinear functions, the Taylor series expansion is utilized and the high-order terms of linearization errors are expressed in an exact way. Furthermore, by solving two Ricatti-like difference equations, the gain matrix can be acquired at each time instant. It is shown that the filtering error is bounded in mean square under some conditions with the aid of stochastic analysis techniques. A numerical example is given to demonstrate the validity of the proposed estimator.     

New results on stability analysis of systems with time-varying delays using a generalized free-matrix-based inequality

This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel–Legendre inequality. An augmented Lyapunov–Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov–Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov–Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method.     

Event-based H∞ filtering for discrete-time Markov jump systems with network-induced delay

The problem of event-based H_∞ filtering for discrete-time Markov jump system with network-induced delay is investigated in this paper. For different jumping modes, different event-triggered communication schemes are constructed to choose which output signals should be transmitted. Through the analysis of network-induced delay’s intervals, the discrete-time system, the event-triggered scheme and network-induced delay are unified into a discrete-time Markov jump filter error system with time-delay. Based on time-delay system analysis method, criteria are derived to guarantee the discrete-time Markov jump error system stochastically stable with an H_∞ norm bound. The correspondent filter and the event-based parameters are also given. A numerical example is given to show that the proposed filter design techniques are effective and event-triggered communication scheme can save limited network resources greatly.     

Dynamic Buckling of Guyed Stacks,Masts and Columns with Constant Inertia and Algebraic Polynomials Generated by use of Operator Tn Attached to Bessel Functions

A new method of analysis of the dynamic critical load of columns, guyed stacks and masts with constant inertia, under the combined action of horizontal loads, axial load and uniformly distributed loads along the vertical axis is presented. The integro-differential formulation of the problem leads to fourth- and fifth- order partial differential equations.In addition to the solution of the equation of motion in expansion series, the new method of solution proposed to solve the fifth-order partial differential equation has led to the differential equation of the plate on elastic foundations in the old Winkler hypothesis. Moreover, the operator T_n, attached to the Bessel functions J_v, has been used to generate a new set of algebraic polynomials.     

Delay-dependent H∞ filtering for discrete singular Markov jump systems with Wiener process and partly unknown transition probabilities

This paper is devoted to the investigation of the delay-dependent H_∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H_∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H_∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper.     

Error analysis in fixed-point digital filters using sign-magnitude truncation

The quantization error of a digital filter employing fixed-point arithmetic with sign-magnitude truncation is analyzed. The effect of coefficient quantization is also included. Exact analyses are presented first for Gaussian, sinusoidal and Gaussian plus sinusoidal inputs. Quasi-linearization is then employed to yield a simple computation method of the output noise variance. The resulting expression contains parameters that depend on the input signal statistics. An upper bound is given that is independent of these statistics. Explicit expressions are given for the second-order sections of the digital filter realized in the D1 and D2 forms together with a general expression for the cascade connection of the second-order sections.     

Kernel recursive generalized mixed norm algorithm

This work studies the problem of kernel adaptive filtering (KAF) for nonlinear signal processing under non-Gaussian noise environments. A new KAF algorithm, called kernel recursive generalized mixed norm (KRGMN), is derived by minimizing the generalized mixed norm (GMN) cost instead of the well-known mean square error (MSE). A single error norm such as l_p error norm can be used as a cost function in KAF to deal with non-Gaussian noises but it may exhibit slow convergence speed and poor misadjustments in some situations. To improve the convergence performance, the GMN cost is formed as a convex mixture of l_p and l_q norms to increase the convergence rate and substantially reduce the steady-state errors. The proposed KRGMN algorithm can solve efficiently the problems such as nonlinear channel equalization and system identification in non-Gaussian noises. Simulation results confirm the desirable performance of the new algorithm.     

A novel finite-time complex-valued zeoring neural network for solving time-varying complex-valued Sylvester equation

A novel finite-time complex-valued zeroing neural network (FTCVZNN) for solving time-varying Sylvester equation is proposed and investigated. Asymptotic stability analysis of this network is examined with any general activation function satisfying a condition or with an odd monotonically increasing activation function. So far, finite-time model studies have been investigated for the upper bound time of convergence using a linear activation function with design formula for the derivative of the error or with variations of sign-bi-power activation functions to zeroing neural networks. A function adaptive coefficient for sign-bi-power activation function (FA-CSBP) is introduced and examined for faster convergence. An upper bound on convergence time is derived with the two components in the function adaptive coefficients of sign-bi-power activation function. Numerical simulation results demonstrate that the FTCVZNN with function adaptive coefficient for sign-bi-power activation function is faster than applying a sign-bi-power activation function to the zeroing neural network (ZNN) and the other finite-time complex-valued models for the selected example problems.     

An explicit-time and explicit-accuracy control for a state-constrained nonstrict-feedback uncertain system based on adaptive fuzzy dynamic-approximation

This article proposes a novel explicit-time and explicit-accuracy adaptive fuzzy control for a state-constrained nonlinear nonstrict-feedback uncertain system. This method can explicitly parameterize the upper bound of settling-time with low initial control input under a bounded initial condition. Meanwhile, this method can also explicitly parameterize the upper bound of accuracy while achieving low control input based on the adaptive fuzzy dynamic-approximation theorem. Firstly, a novel generalized explicit-time stability system is proposed by introducing the boundary gain term to render the time-parameter explicit, this method can solve the input conservatism problem caused by the unbounded-state gain term of traditional fixed/prdefined-time function. Then, according to the universal fuzzy approximation theorem, the novel dynamic relationship of adaptive fuzzy logic system between approximation error and adaptive parameters is presented. This relationship can lead to the adaptive fuzzy dynamic-approximation theorem, and an adaptive law designed by this theorem can realize the Lyapunov stability of adaptive control system under a Lasalle invariant set. In the end, a novel adaptive fuzzy control scheme is proposed by the generalized explicit-time function and adaptive fuzzy dynamic-approximation theorem. This scheme can achieve the explicit-time stability by the human-like activation function, and the accuracy can be parameterized by Lyapunov synthesis. Compared with other existing fixed/prdefined-time adaptive fuzzy control methods, the proposed explicit-time and explicit-accuracy controller achieves a significant reduction in the initial control input. Theoretical analysis and simulation results validate the effectiveness of the proposed method.     

Truncation error analysis in computing of SEP and SEP floor for partially coherent receiver of MPSK signals over composite fading channels

In this paper, we analyze detection of multilevel phase-shift keying (MPSK) signals transmitted over a Gamma shadowed Nakagami-m fading channel. We derive novel analytical expression, in terms of Meijer’s G function, for Fourier coefficients of the probability density function of the received signal composite phase. Under the assumption of the imperfect reference signal extraction in the receiver, which is performed from the pilot signal, the analytical expression is derived for the symbol error probability (SEP) in the form of convergent series. The existence of the error floor is identified, and expression for its computation is provided. Mathematical proofs for convergence of Fourier series are provided for both SEP and SEP floor, and novel expressions of upper bounds for truncation errors are derived in terms of elementary mathematical functions. The convergence rate of the derived expressions is examined. Numerical results are confirmed independently by Monte-Carlo simulations.     

Positive-real systems under lossless transformations: Invariants and reduced order models

In this paper, positive-real systems under lossless positive-real transformations are investigated. Let G(s) be the transfer function matrix of a continuous-time positive-real system of order n and F(s) a lossless transfer function of order n_F. We prove here that the lossless positive-real transformed system, i.e. G(F(s)), is also positive-real. Furthermore, the stochastic balanced representation of positive-real systems under lossless positive-real transformations is considered. In particular, it is proved that the positive-real characteristic values π_j of G(F(s)) are the same of G(s) each with multiplicity n_F, independently from the choice of F(s). This property is exploited in the design of reduced order models based on stochastic balancing. Finally, the proposed technique is a passivity preserving model order reduction method, since it is proven that the reduced order model of G(F(s)) is still positive-real. An error bound for truncation related to the invariants π_j is also derived.     

Generalized filtering of one-sided Lipschitz nonlinear systems under measurement delays

This paper addresses the filtering problem for the one-sided Lipschitz nonlinear systems under measurement delays and disturbances using a generalized observer. A generalized architecture for filtering of the one-sided Lipschitz nonlinear systems with output delays is explored, which exhibits diverging manifolds, namely, the conventional static-gain filter and the dynamical filter, and can be employed to render robust stability of the filtering error dynamics. A matrix inequality based framework is obtained by employing a Lyapunov?Krasovskii (LK) functional, whose derivative is exploited through Jensen's inequality, one-sided Lipschitz condition, quadratic inner-boundedness inequality and range of the measurement delay, resulting into L₂ stability for the filtering error system. Generalized filter design for the Lipschitz nonlinear systems with delayed outputs and specific results for the delay-dependent and delay-rate-independent filtering schemes for the one-sided Lipschitz nonlinear systems are deduced from the proposed approach. Convex optimization techniques are employed to achieve a solution for the nonlinear constraints through linear matrix inequalities by employing cone complementary linearization approach. Illustrative numerical examples to demonstrate the effectiveness of proposed method are provided.     

Study of flow rate induced measurement error in flow-through nano-hole plasmonic sensor

Flow-through gold film perforated with periodically arrayed sub-wavelength nano-holes can cause extraordinary optical transmission (EOT), which has recently emerged as a label-free surface plasmon resonance sensor in biochemical detection by measuring the transmission spectral shift. This paper describes a systematic study of the effect of microfluidic field on the spectrum of EOT associated with the porous gold film. To detect biochemical molecules, the sub-micron-thick film is free-standing in a microfluidic field and thus subject to hydrodynamic deformation. The film deformation alone may cause spectral shift as measurement error, which is coupled with the spectral shift as real signal associated with the molecules. However, this microfluid-induced measurement error has long been overlooked in the field and needs to be identified in order to improve the measurement accuracy. Therefore, we have conducted simulation and analytic analysis to investigate how the microfluidic flow rate affects the EOT spectrum and verified the effect through experiment with a sandwiched device combining Au/Cr/Si₃N₄ nano-hole film and polydimethylsiloxane microchannels. We found significant spectral blue shift associated with even small flow rates, for example, 12.60 nm for 4.2 μl/min. This measurement error corresponds to 90 times the optical resolution of the current state-of-the-art commercially available spectrometer or 8400 times the limit of detection. This really severe measurement error suggests that we should pay attention to the microfluidic parameter setting for EOT-based flow-through nano-hole sensors and adopt right scheme to improve the measurement accuracy.     

The upper bound of minimum moment of inertia of equi-area convex domains

The problem of nontrivial bounds of moments of inertia for plane configurations is formulated. The Winternitz theorem is generalized to establish the bounds of the ratio of the Nth moment of areas of two subdomains created by any of the centroidal axes of a convex domain. For convex equi-area domains the upper bound of the minimum moment of inertia with respect to a general coordinate system is discussed. In particular, for the cases of the origin of coordinate axes coinciding with the centroid and coinciding with a point on the periphery, the upper bound of the minimum moment of inertia is proved to belong to an equilateral triangle and an isosceles 120° triangle, respectively.     

A dynamically event-triggered approach to recursive filtering with censored measurements and parameter uncertainties

In this paper, a dynamically event-triggered filtering problem is investigated for a class of discrete time-varying systems with censored measurements and parameter uncertainties. The censored measurements under consideration are described by the Tobit measurement model. In order to save the communication energy, a dynamically event-triggered mechanism is utilized to decide whether the measurements should be transmitted to the filter or not. The aim of this paper is to design a robust recursive filter such that the filtering error covariance is minimized in certain sense for all the possible censored measurements, parameter uncertainties as well as the effect induced by the dynamically event-triggered mechanism. By means of the mathematical induction, an upper bound is firstly derived for the filtering error covariance in terms of recursive matrix equations. Then, such an upper bound is minimized by designing the filter gain properly. Furthermore, the boundedness is analyzed for the minimized upper bound of the filtering error covariance. Finally, two numerical simulations are exploited to demonstrate the effectiveness of the proposed filtering algorithm.     

Robust non-fragile filtering for networked systems with distributed variable delays

This paper is concerned with the robust non-fragile filtering for a class of networked systems with distributed variable delays. We model such a complex delay system with an augmented switched system. For the filtering implementation uncertainty, a stochastic variable is employed to indicate random occurrence of the filter gain change, and a norm bound to measure the change size. The suitably weighted measurements are proposed for filter performance improvement, instead of direct use of the measurements themselves which may have significant delays and degrade the performance. With some improved stability and l₂ gain analysis for the switched systems, a new sufficient condition is obtained such that the filtering error system is exponentially stable in the mean square sense and achieves a prescribed _H∞$H_{\infty }$ performance level. A numerical example is given to show the effectiveness of the proposed design.     

Probability of error in CPSK systems with intersymbol interference and additive noise

A simple lower bound, an upper bound and a simple approximation to the upper bound on the probability of error for coherent phase-shift-keyed (CPSK) systems operating in the presence of intersymbol interference and additive noise are obtained. The additive noises in the in-phase channel and the quadrature channel are assumed to be independent, and are independent of the signal, but not restricted to be Gaussian. The approximation to the upper bound is four times the lower bound, hence the tightness of these bounds is uniform for all cases. This fact and the simplicity of the bounds make these bounds a useful system design tool. Numerical examples for quaternary and octonary systems are presented and compared to known results.     

Particle filter with Markovian packet dropout and time delay

This technical note is concerned with particle filter for the discrete-time nonlinear networked control system. First, modified particle filter algorithm with Markovian packet dropout and time delay is proposed, and its error covariance is benchmarked by Markovian Cramér-Rao lower bound. Second, an upper bound of the Markovian Cramér-Rao lower bound is presented for some special nonlinear networked systems. Third, some necessary conditions for the boundness of error covariance are given by obtaining some sufficient conditions for the bounded Markovian Cramér-Rao lower bound. Finally, numerical examples are presented to illustrate the efficiency of proposed particle filter.