On controllability of discrete-time bilinear systems

In this paper, necessary and sufficient conditions for the controllability of a class of discrete-time bilinear systems are proposed, which extend the existing results and show that the controllability counterexample in [1] that is derived by Euler discretization of an uncontrollable bilinear system, is a special case of the necessary and sufficient conditions.     

Sampling and control of switched linear systems

In this paper, we address the sampling and control issues for switched linear systems. Under synchronous switching and piecewise constant control, a continuous-time switched system is naturally related to a discrete-time sampled-data system. We prove that, with almost any sampling rate, the controllable subspace will be preserved for a switched linear system. We also investigate the possibility of achieving controllability using regular switching mechanisms. We show that, to achieve controllability for a switched linear system, it is sufficient to use cyclic and synchronous switching paths and constant control laws.     

Approximate controllability of nonlinear stochastic evolution systems with time-varying delays

In this paper, the approximate controllability of nonlinear stochastic evolution time-varying delay systems with preassigned responses is studied. The necessary conditions for controllability results of nonlinear systems are not associated with linear systems. No compactness assumptions are imposed in the main results.     

可变参量水槽系统中两列孤波的相互作用

基于(1+1)维非均匀非线性薛定谔方程,数值研究了可变参量水槽系统中两列孤波的相互作用。结果表明,两列孤波在强非线性相互作用下具有稳定的演化。且这样稳定的演化具有可控的参数。     

Fading memory and stability

The conditions under which discrete-time nonlinear affine systems possess fading memory are explored. A sufficient condition is given based on discrete-time Lyapunov theory; whereas a necessary condition is provided based on the relationship between the stability and the continuity of this system.     

H∞ output-feedback control for discrete-time switched linear systems via asynchronous switching

In this paper, we consider the H_∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l₂-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l₂-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results.     

Leader-following consensus of nonlinear discrete-time multi-agent systems with limited communication channel capacity

This paper considers the problem of the leader-following consensus of generally nonlinear discrete-time multi-agent systems with limited communication channel capacity over directed fixed communication networks. The leader agent and all follower agents are with multi-dimensional nonlinear dynamics. We propose a novel kind of consensus algorithm for each follower agent based on dynamic encoding and decoding algorithms and conduct a rigorous analysis for consensus convergence. It is proved that under the consensus algorithm designed, the leader-following consensus is achievable and the quantizers equipped for the multi-agent systems can never be saturated. Furthermore, we give the explicit forms of the data transmission rate for the connected communication channel. By properly designing the system parameters according to restriction conditions, we can ensure the consensus and communication efficiency with merely one bit information exchanging between each pair of adjacent agents per step. Finally, simulation example is presented to verify the validity of results obtained.     

Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations

The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.     

H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H_∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H_∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.     

Group controllability of two-time-scale multi-agent networks

As a basic concept in modern control theory, controllability reveals the fundamental structural characteristics of a dynamic system, and it also plays an important part in the analysis and control of a dynamic system. With the increasing complexity of multi-agent systems, the multi-agent networks can be divided into some subnetworks in terms of time scales. This paper concentrates on the group controllability of two-time-scale multi-agent networks, establishes the necessary and sufficient criterion of group controllability based on singular perturbation methods, and deduces easy-to-use group controllability criteria by using matrix theory and graph theory. Lastly, a simulation example is presented to illustrate the effectiveness of the proposed methods.     

(ω)性质的摄动

一般地,若T满足(ω)性质,即使K是有限秩算子或紧算子,T+K也不一定有(ω)性质.根据本质逼近点谱的变形与一致可逆算子定义的谱集,给出了(ω)性质及其摄动的充要条件,并将所得结论应用于代数拟A类算子.     

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.     

Absolute stability and Lyapunov–Krasovskii functionals for switched nonlinear systems with time-delay

We derive conditions for the existence of Lyapunov–Krasovskii functionals for a number of classes of nonlinear switched systems with time-delay. In particular, we first give conditions for systems of retarded type that relax those recently described in Sun and Wang (2013) [18]. Using similar techniques, related results are then derived for coupled differential-difference systems and for systems of neutral type. Finally, we briefly note some corresponding results for discrete-time systems.     

Widely linear estimation for multisensor quaternion systems with mixed uncertainties in the observations

The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.     

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.     

Dissipative observers for discrete-time nonlinear systems

This paper addresses the problem of designing a state observer for a class of nonlinear discrete-time systems using the dissipativity theory. We show that the dissipative observation methodology, originally proposed by one of the authors for continuous-time nonlinear systems, can be extended to the discrete-time case. For constructing a convergent observer, the methodology is applied to the nonlinear estimation error dynamics, which is decomposed into a discrete-time Linear Time-Invariant (LTI) subsystem in the forward loop, connected to a time-varying static nonlinearity in the feedback loop. In order to assure asymptotic stability of the closed-loop, complementary dissipativity conditions are imposed on each of the subsystems: (i) the static nonlinearity is required to be dissipative with respect to a quadratic supply rate, and (ii) the observer gains are designed such that the LTI system is dissipative with respect to a complementary supply rate. As in the continuous time framework, the proposed method includes as special cases, unifies and generalizes some observer design methods proposed previously in the literature. A great advantage of the Dissipative Observer Design Method proposed here is that it leads to Matrix Inequalities for the design of the observer gains, and these can be usually converted into Linear Matrix Inequalities (LMI’s). The results are illustrated using Chua’s Chaotic system.     

Parameter estimation for an input nonlinear state space system with time delay

This paper researches parameter estimation problems for an input nonlinear system with state time-delay. Combining the linear transformation and the property of the shift operator, the system is transformed into a bilinear parameter identification model. A gradient based and a least squares based iterative parameter estimation algorithms are presented for identifying the state time-delay system. The simulation results confirm that the proposed two algorithms are effective and the least squares based iterative algorithm has faster convergence rates than the gradient based iterative algorithm.     

Distributed event-triggered target tracking under cyber attacks

Distributed target tracking is an important problem in sensor networks (SNs). In this paper, the problem of distributed target tracking is addressed under cyber-attacks for targets with discrete-time and continuous-time nonlinear dynamics. Two distributed filters are obtained for every node of the SN to estimate the states of a general class of nonlinear targets which can be seen in many practical applications. Compared with the existing results in the literature, the network topology of the SN is assumed to be subjected to the denial-of-service attack such that the communication links among sensor nodes are paralyzed or destroyed by this kind of attack. Moreover, the proposed algorithms are designed based on an event-triggered communication strategy that means the frequency of information transmission and unnecessary resource consumption are significantly reduced. The presented algorithms’ stability is also analyzed in the presence of noise to achieve secure event-triggered target tracking in mean-square. Two simulation examples are utilized to demonstrate the efficiency of the proposed event-triggered algorithms.     

Discrete-time adaptive fuzzy speed regulation control for induction motors with input saturation via command filtering

A discrete-time adaptive fuzzy control method is introduced to achieve the speed regulation for induction motors (IMs) with input saturation via command filtering in this paper. First, the continuous model of IMs drive system is transformed into discrete-time form by using Euler formula. Then, the fuzzy logic systems are used to approximate the unknown nonlinear functions in the discrete-time drive system. In addition, the command filtering control method is introduced to overcome the “explosion of complexity” problem in the design process of traditional backstepping method. It is verified that all the closed-loop signals are bounded and the outputs can track the given reference signals well. Finally, simulation results illustrate the validity of the discrete-time control method.     

On direct adaptive control design for nonlinear discrete-time uncertain systems

In this paper, we develop a direct adaptive control framework for adaptive stabilization of the MIMO nonlinear uncertain systems, which can be represented as discrete-time normal form with input-to-state zero dynamics. The framework is Lyapunov-based and guarantees partial stability of the closed-loop systems, such that the adaptation of the feedback gains can stabilize the closed-loop system without the knowledge of the system parameters. In addition, our results show that the adaptive feedback laws can be characterized by Kronecker calculus. Two numerical examples are given to demonstrate the efficacy of the proposed framework.