Observer-based output feedback control for networked systems with dual-channel event-triggered sampling and quantization

This paper investigates the problem of observer-based output feedback control for linear networked systems with dual-channel event-triggered mechanisms and quantization. Both continuous-time and discrete-time event detection cases are discussed. In the continuous-time case, the stability of observer error dynamics and closed-loop system are analyzed respectively, and it is proved that Zeno behavior would not occur. In order to approach engineering practice, in the discrete-time case, two types of network attacks including denial-of-service (DoS) and fault data injection (FDI) attacks are considered, whose nature property is characterized by Bernoulli variables. By combining these factors and transmission delay, a novel augmented system model is proposed, and some sufficient conditions are derived based on Lyapunov functional approach and linear matrix inequalities (LMIs). Compared with the existing results, this framework is more comprehensive and practical, and the global uniform ultimate boundedness of closed-loop systems can be guaranteed. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method.     

Exponential stabilization of switched linear systems subject to actuator saturation with stabilizable and unstabilizable subsystems

This paper is concerned with the exponential stabilization of switched linear systems subject to actuator saturation with both stabilizable subsystems and unstabilizable subsystems for continuous-time case and discrete-time case, respectively. Sufficient conditions for the exponential stabilization under dwell time switching under the cases of continuous-time and discrete-time are established by using a novel class of multiple time-varying Lyapunov function. The existence conditions for stabilizing controllers are presented in terms of linear matrix inequalities (LMIs) for the continuous-time case and the discrete-time case, respectively. Two optimization problems are proposed for obtaining the maximal attraction region. The problem of exponential stabilization for switched system subject to actuator saturation with asynchronous switching controller is also studied. Several numerical examples are presented to prove the validity of the obtained results.     

A Dual Approach to a Linear Smoothing Problem

In this paper, the continuous-time linear Gaussian smoothing problem is investigated by utilizing a dual approach. It is shown that the smoothing problem is a dual of an optimal regulator with a jump condition on the trajectory. By solving the dual optimal control problem, basic results established earlier on this smoothing problem are derived in a simpler way. Results are also obtained for the discrete-time linear smoothing Gaussian problem.     

Stabilization of networked periodic piecewise linear systems under asynchronous switching with packet dropouts

In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples.     

Quadratic stability analysis and robust distributed controllers design for uncertain spatially interconnected systems

This paper is concerned with the quadratic stability analysis and robust distributed controllers design of both continuous-time and discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). The well-posedness, quadratic stability, and contractiveness of USISs are properly defined for the first time. A sufficient condition employing the given system matrices is established to check the well-posedness, quadratic stability and contractiveness. This condition is simpler than the existing conditions based on the decomposition of system matrices. Based on the new condition derived, a sufficient condition is given for the existence of robust distributed controllers and a constructive method is then presented for the design of robust distributed controllers. The advantage of the proposed constructive approach is that it employs the given system matrices while the existing methods conduct the bilinear transformation on these matrices when design controllers, and consequently, the constructive approach in this paper is computationally more efficient than the existing methods. Several examples are included to demonstrate the simplicity, efficiency and applicability of the derived theoretical results.     

Non-fragile control of positive Markovian jump systems

This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

离散区间2-D系统的二次稳定性分析

本文针对离散区间2-D系统的二次稳定性问题,给出了线性矩阵不等式形式的判定条件。所得结论利用Matlab可以非常方便地求解,同时条件的必要性表明在某些情况下结论的保守性小。所给出的数值算例表明该判定条件可以有效地判定离散区间2-D系统是否二次稳定。     

Implicit and explicit discrete-time realizations of the robust exact filtering differentiator

This paper presents explicit and implicit discrete-time realizations for the robust exact filtering differentiator, aiming to facilitate an adequate posterior implementation structure in digital devices. This paper firstly presents an analysis of an explicit discrete-time realization of the filtering differentiator based on linear systems’ exact discretization with a zero-order holder. For this case, however, high-order terms in the filter dynamics may cause instability of the estimation error for signals with unbounded derivatives. Hence, two other new discrete-time realizations of the filtering differentiator are derived by removing some high-order terms in the filter dynamics. The first one is an explicit discrete-time realization, while the second one is implicit. After a finite time, both preserve the accuracy of the continuous-time robust exact filtering differentiator in the presence of measurement noise. For each proposed discrete-time scheme, a stability analysis based on homogeneity is provided. Finally, the simulation results include comparisons between the proposed implicit and explicit discrete-time realizations with other existing schemes. These numerical studies highlight that the implicit scheme supersedes the explicit one, consistent with the implicit and explicit realizations of other continuous-time algorithms.     

Modeling and solution of two-dimensional input time-delay system

The discrete-time model of the two-dimensional continuous-time input time-delay system is newly presented in this paper, and the solution of the continuous-time input time-delay system is then solved based on the newly presented discrete-time model. The presented discrete-time model significantly facilitates analysis and design of a system when it faces the unavoidable inherent time delay and the computation time delay which can be modeled as a part of delay at the system input, in practice.     

Network-based PI control for output tracking of continuous-time systems with time-varying sampling and network-induced delays

For a continuous-time linear system with constant reference input, the network-based proportional-integral (PI) control is developed to solve the output tracking control problem by taking time-varying sampling and network-induced delays into account. A traditional PI control system is introduced to obtain the equilibriums of state and control input. Using the equilibriums, a discrete-time PI tracking controller in a network environment is constructed. The resulting network-based PI control system is described by an augmented system with two input delays and the output tracking objective is transformed into ensuring asymptotic stability of the augmented system. A delay-dependent stability condition is established by a discontinuous augmented Lyapunov–Krasovskii functional approach. The PI controller design result of in-wheel motor as a case study is provided in terms of linear matrix inequalities. Matlab simulation and experimental results resorting to a test-bed for ZigBee-based control of in-wheel motor are given to validate the proposed method.     

Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems.     

General 9-instant discrete-time Zhang neural network for time-dependent applications

Zhang neural network (ZNN) is widely applied to solving time-dependent problems. For the sake of the implementation on the digital hardware platform, ZNN models need to be discretized. In this paper, as a further study of Zhang et al. discretization (ZeaD) formulas, a novel general 9-instant ZeaD formula is presented, and clear constraints are firstly given with proof. To evaluate the presented 9-instant ZeaD formula, three continuous-time models for time-dependent matrix inversion and pseudoinversion are presented with the help of Getz-Marsden dynamic system (GMDS) and ZNN. Then the corresponding discrete-time models are obtained by using the 9-instant ZeaD formula. According to the comparison experiments, the 9-instant ZeaD formula is substantiated to be effective and consistent with the theory. Furthermore, the problem of mobile angle-of-arrival (AoA) localization is investigated as a more specific and practical problem. In order to overcome the singularity problem of the tangent function in the representation of the AoA localization system, a new representation with sine and cosine functions is presented. Similarly, the continuous-time model is derived and discretized. Through comparison experiments, the discrete-time model obtained by the 9-instant ZeaD formula achieves desirable results, which further show the efficacy of the 9-instant ZeaD formula.     

Cooperative output regulation problem of multi-agent systems with stochastic packet dropout and time-varying communication delay

In this paper, we deal with the cooperative output regulation problem of linear multi-agent systems on a directed network topology subject to both stochastic packet dropout and time-varying communication delay. On the basis of introducing a queuing mechanism, a distributed state feedback control algorithm is proposed. Then the continuous-time multi-agent systems with piece-wise constant control are converted into discrete-time systems. Under some standard assumptions, the necessary and sufficient conditions under which the tracking errors of followers approach to the origin asymptotically are proposed for different exosystems. Finally, the proposed results are verified via two examples.     

Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach

This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.     

Cyclic gradient based iterative algorithm for a class of generalized coupled Sylvester-conjugate matrix equations

This paper focuses on the numerical solution of a class of generalized coupled Sylvester-conjugate matrix equations, which are general and contain many significance matrix equations as special cases, such as coupled discrete-time/continuous-time Markovian jump Lyapunov matrix equations, stochastic Lyapunov matrix equation, etc. By introducing the modular operator, a cyclic gradient based iterative (CGI) algorithm is provided. Different from some previous iterative algorithms, the most significant improvement of the proposed algorithm is that less information is used during each iteration update, which is conducive to saving memory and improving efficiency. The convergence of the proposed algorithm is discussed, and it is verified that the algorithm converges for any initial matrices under certain assumptions. Finally, the effectiveness and superiority of the proposed algorithm are verified with some numerical examples.     

A relaxed MSIO iteration algorithm for solving coupled discrete Markovian jump Lyapunov equations

In this paper, combining the multi-step Smith-inner-outer (MSIO) iteration framework with some tunable parameters, a relaxed MSIO iteration method is proposed for solving the Sylvester matrix equation and coupled Lyapunov matrix equations (CLMEs) in the discrete-time jump linear systems with Markovian transitions. The convergence properties of the relaxed MSIO iteration method are investigated, and the choices of the parameters are also discussed. In order to accelerate the convergence rate of the relaxed MSIO iteration method for solving the CLMEs, a current-estimation-based and a weighted relaxed MSIO iteration algorithms are presented, respectively. Finally, several numerical examples are given to verify the superiorities of the proposed relaxed algorithms.     

A new approach to average consensus problems with multiple time-delays and jointly-connected topologies

This paper investigates average consensus problem in networks of continuous-time agents with delayed information and jointly-connected topologies. A lemma is derived by extending the Barbalat's Lemma to piecewise continuous functions, which provides a new analysis approach for switched systems. Then based on this lemma, a sufficient condition in terms of linear matrix inequalities (LMIs) is given for average consensus of the system by employing a Lyapunov approach, where the communication structures vary over time and the corresponding graphs may not be connected. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.     

Sliding mode control for uncertain discrete-time systems with Markovian jumping parameters and mixed delays

This paper is concerned with the robust sliding mode control (SMC) problem for a class of uncertain discrete-time Markovian jump systems with mixed delays. The mixed delays consist of both the discrete time-varying delays and the infinite distributed delays. The purpose of the addressed problem is to design a sliding mode controller such that, in the simultaneous presence of parameter uncertainties, Markovian jumping parameters and mixed time-delays, the state trajectories are driven onto the pre-defined sliding surface and the resulting sliding mode dynamics is stochastically stable in the mean-square sense. A discrete-time sliding surface is firstly constructed and an SMC law is synthesized to ensure the reaching condition. Moreover, by constructing a new Lyapunov–Krasovskii functional and employing the delay-fractioning approach, a sufficient condition is established to guarantee the stochastic stability of the sliding mode dynamics. Such a condition is characterized in terms of a set of matrix inequalities that can be easily solved by using the semi-definite programming method. A simulation example is given to illustrate the effectiveness and feasibility of the proposed design scheme.     

Sampled-data predictive control for uncertain jump systems with partly unknown jump rates and time-varying delay

This paper presents a sampled-data predictive control strategy for a class of uncertain continuous-time Markovian jump linear system (MJLS) with time-varying delay. The system under consideration covers MJLS with completely known jump rates and arbitrary switched linear system. The predictive formulation utilizes both off-line and on-line optimization paradigms. The feasibility of the control scheme and the stability of the closed-loop system are investigated by introducing a modified stochastic invariant ellipsoid. The conditions for the existence of a stabilizing optimal controller for the underlying system are obtained via the semi-definite programming (SDP). A numerical example is given to verify efficiency and potential of the developed approach.