New results on linear parameter-varying time-delay systems

A class of linear parameter-varying time-delay systems where the state-space matrices depend on time-varying parameters and the time-delay is unknown but bounded is considered. Both notions of quadratic stability (using a single quadratic Lyapunov-Krasovskii function) and affine quadratic stability (using parameter-dependent Lyapunov-Krasovskii functions) are investigated. LMI-based delay-independent and delay-dependent conditions are derived for stability testing. Then, state-feedback controllers are designed which guarantee quadratic stability and an induced L₂-norm bound. We use a parameter-independent quadratic Lyapunov-Krasovskii function for the case of dynamic output feedback control to develop LMI-based solvability conditions which are evaluated at the extreme points of the admissible parameter set. Numerical examples are presented.     

Robust delay-dependent H∞ filtering for uncertain Takagi–Sugeno fuzzy neutral stochastic time-delay systems

This paper addresses the robust H_∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H_∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H_∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.     

Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays

In this paper, new results are established for the delay-independent and delay-dependent problems of dissipative analysis and state-feedback synthesis for a class of nonlinear systems with time-varying delays with polytopic uncertainties. This class consists of linear time-delay systems subject to nonlinear cone-bounded perturbations. Both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequality-based feasibility tests. The developed results in this paper for the nominal system encompass available results on H_∞ approach, passivity and positive realness for time-delay systems as special cases. All the sufficient stability conditions are cast. Robust dissipativity as well as dissipative state-feedback synthesis results are also derived. Numerical examples are provided to illustrate the theoretical developments.     

Robust fault detection for a class of nonlinear time-delay systems

In this paper, the robust fault detection filter (RFDF) design problems are studied for nonlinear time-delay systems with unknown inputs. Firstly, a reference residual model is introduced to formulate the robust fault detection filter design problem as an H_∞ model-matching problem. Then appropriate input/output selection matrices are introduced to extend a performance index to the time-delay systems in time domain. The reference residual model designed according to the performance index is an optimal residual generator, which takes into account the robustness against disturbances and sensitivity to faults simultaneously. Applying robust H_∞ optimization control technique, the existence conditions of the robust fault detection filter for nonlinear time-delay systems with unknown inputs are presented in terms of linear matrix inequality (LMI) formulation, independently of time delay. An illustrative design example is used to demonstrate the validity and applicability of the proposed approach.     

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.     

Stability and dissipative analysis for a class of stochastic system with time-delay

This paper deals with the stability and dissipative problem of a class of stochastic hybrid system. The system under study involves Markovian jump, impulsive effects and time delay, which are often encountered in practice and are the sources of instability. Our attention is focused on analysis of whether the stochastic hybrid system with time-delay is stochastically asymptotically stable and strictly (Q, S, R) dissipative. By introducing an extra artificial time instance, the equivalent system is obtained and the sufficient conditions are derived by using linear matrix inequality (LMI) techniques. The main results of this paper unify the existing results on H_∞ control.     

Sampled-data control for time-delay systems

The sampled-data systems are hybrid ones involving continuous time and discrete time signals, which makes the traditional analysis and synthesis methodologies of time-delay systems unable to be directly used in the cases of hybrid systems with time-delay. The primary disadvantages of current design techniques of sampled-data control are their inabilities to deal effectively with time-delay and the model uncertainty. In this paper, we generalized the analysis methodology of time-delay systems to that of the hybrid systems with time-delay and uncertainty, which developed a design procedure of sampled-data control for time-delay systems. Asymptotic stability of the time-delay hybrid systems was developed. The time-delay dependent robust sampled-data control for the time-varying delay of an uncertain linear system was then discussed. The results were described as linear matrix inequalities, which can be solved using newly released LMITool.     

Discrete Razumikhin-type stability theorems for stochastic discrete-time delay systems

By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined.     

Necessary conditions of exponential stability for a class of linear uncertain systems with a single constant delay

In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples.     

Stochastic synchronization of semi-Markovian jump chaotic Lur’e systems with packet dropouts subject to multiple sampling periods

This paper is concerned with the problem of stochastic synchronization for semi-Markovian jump chaotic Lur’e systems. Firstly, packet dropouts and multiple sampling periods are both considered. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original system is transformed to a stochastic time-delay system. Secondly, by getting the utmost out of the usable information on the actual sampling pattern, the probability distribution values of stochastic delay taking values in m given intervals can be explicitly obtained. Then, a newly augmented Lyapunov-Krasovskii functional is constructed. Based on that, some sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure the stochastic stability of the error system, and thus, the master system stochastically synchronize with the slave system. Finally, the effectiveness and potential of the obtained results is verified by a simulation example.     

On delay-dependent stabilization analysis for the switched time-delay systems with the state-driven switching strategy

For the switched time-delay systems, the delay-dependent stability criteria will be derived under a state-driven switching law. A linear state transformation was introduced to transfer the switched time-delay system. On delay dependent stabilization analysis, we apply the Lyapunov-Krasovskii functionals to analyze the stabilization of the switched time-delay systems. This method can be applied to cases when all individual switched systems are unstable. Finally, one example is exploited to illustrate the proposed schemes.     

New robust delay-dependent stability and H∞ analysis for uncertain Markovian jump systems with time-varying delays

This paper deals with the problems of robust delay-dependent stability and H_∞ analysis for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, an improved delay-range-dependent stability condition for Markovian jump systems is proposed by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and a sufficient condition is derived from the H_∞ performance. Numerical examples are provided to demonstrate efficiency and reduced conservatism of the results in this paper.     

Stability and L2-gain analysis of switched input delay systems with unstable modes under asynchronous switching

We consider the stability and L₂-gain analysis problem for a class of switched linear systems. We study the effects of the presences of input delay and switched delay in the feedback channels of the switched linear systems with an external disturbance. By contrast with the most of the contributions available in literatures, we do not require that all the modes of the switched system are stable when input delay appears in the feedback input. By reaching a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and permitting the increasing of the multiple Lyapunov functionals on all the switching times, the solvable conditions of exponential stability and weighted L₂-gain are developed for the switched system under mode-dependent average dwell time scheme (MDADT). Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.     

Delay-dependent stochastic stability and H∞ analysis for time-delay systems with Markovian jumping parameters

This paper studies the problem of the stochastic stability and H_∞ disturbance attenuation for linear continuous-time time-delay systems that possess randomly Markovian jumping parameters. A delay-dependent sufficient condition on the stochastic stability with given H_∞ performance is proposed using the stochastic Lyapunov–Krasovskii stability theory. The conditions are formulated as a set of coupled linear matrix inequalities.     

Modeling and stabilization of networked control systems with bounded packet dropouts and occasionally missing control inputs subject to multiple sampling periods

The paper is concerned with the modeling and stabilization problem of networked control systems under simultaneous consideration of bounded packet dropouts and occasionally missing control inputs. In particular, the focus of the paper is to capture the case where the packet dropouts and control inputs missing are subject to multiple sampling periods, and not periodic as in existing results. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original linear system is firstly transformed to a switched stochastic time-delay system. Meanwhile, the probability distribution values of stochastic delay taking values in m(m ≥ 2) given intervals can be explicitly obtained, which is of vital importance to analyse the stabilization problem of considered system. Secondly, by means of the average dwell time technique, some sufficient conditions in terms of linear matrix inequalities for the existence of desired stabilizing controller are derived. Finally, an illustrative example is given to illustrate the effectiveness of the proposed stabilizing controller and some less conservative results are obtained.     

Delay-dependent dissipative control for linear time-delay systems

This paper deals with the problem of delay-dependent dissipative control for a class of linear time-delay systems. We develop the design methods of dissipative static state feedback and dynamic output feedback controllers such that the closed-loop system is quadratically stable and strictly (Q,S,R)-dissipative. Sufficient conditions for the existence of the quadratic dissipative controllers are obtained by using linear matrix inequality (LMI) approach. Furthermore, a procedure of constructing such controllers from the solutions of LMIs is given. It is shown that the solvability of a dissipative controller design problem is implied by the feasibility of LMIs. The main results of this paper unify the existing results on H^∞ control and passive control.     

Event-triggered controller design for positive T-S fuzzy systems with random time-delay

This paper is concerned with the design of event-triggered controller for positive Takagi-Sugeno (T-S) fuzzy systems with a random time-delay. The random time-delay is described as a Markov process. A controller switched at different event-triggered instant is proposed. By constructing a new event-triggered instant-dependent linear co-positive Lyapunov function, the design criteria of event-triggered controller is derived to ensure the positivity and stability of the closed-loop system. These criteria can be solved by linear programming (LP) technique. A positive lower bound on the inter-execution time is ensured, which means that there is Zeno-free phenomenon. Finally, the simulation has demonstrated the effectiveness and merit of the proposed results.     

L1-gain analysis and control of impulsive positive systems with interval uncertainty and time delay

This paper investigates L₁-gain analysis and control of impulsive positive systems (IPSs) with interval uncertainty and time delay. For different types of impulsive effect, by means of the Razumikhin techniques and Lyapunov function theory, conditions are developed for guaranteeing the robust exponential stability with L₁-gain performance. Then the positive stabilization with L₁-gain performance is also addressed for IPSs with interval uncertainty and time delay through the state feedback control. In addition, the way to explore the minimum L₁-gain is discussed. All the obtained conditions can be easily inspected by the linear programming (LP) method when some parameters are preset. Finally, simulations are provided to demonstrate the validity of the theoretical results.     

Delay-independent stabilization of linear systems with time-varying delayed state and uncertainties

The problem of robust stabilization for a class of dynamic systems with time-varying state delay as well as parametric and input uncertainties is considered in this paper. Several delay-independent stabilizability criteria and memoryless state feedback controllers are presented to guarantee the asymptotic stability of the closed-loop uncertain time-delay systems. It is shown that if all uncertainties and delay terms are matched, then the mentioned systems can always be stabilized, or can be stabilized with a specified decaying rate.