This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

In this paper, the problem of robust fault tolerant control for a class of singular systems subject to both time-varying state-dependent nonlinear perturbation and actuator saturation is investigated. A sufficient condition for the existence of a fixed-gain controller is first proposed which guarantees the regularity, impulse-free and stability of the closed-loop system under all possible faults. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. An adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online. Both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart. An example is included to illustrate the proposed procedures and their effectiveness.

Fault tolerant control for singular systems with actuator saturation and nonlinear perturbationFault tolerant control for singular systems with actuator saturation and nonlinear perturbation.

This paper proposes a new non-fragile stochastic control method to investigate the robust sampled-data synchronization problem for uncertain chaotic Lurie systems (CLSs) with time-varying delays. The controller gain fluctuation and time-varying uncertain parameters are supposed to be random and satisfy certain Bernoulli distributed white noise sequences. Moreover, by choosing an appropriate Lyapunov-Krasovskii functional (LKF), which takes full advantage of the available information about the actual sampling pattern and the nonlinear condition, a novel synchronization criterion is developed for analyzing the corresponding synchronization error system. Furthermore, based on the most powerful free-matrix-based integral inequality (FMBII), the desired non-fragile sampled-data estimator controller is obtained in terms of the solution of linear matrix inequalities. Finally, three numerical simulation examples of Chua's circuit and neural network are provided to show the effectiveness and superiorities of the proposed theoretical results.

Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation.

This paper studies the problems of stability and stabilization for a class of singular switching semi-Markovian jump systems. The general transition rates in the semi-Markov process cover completely unknown and uncertain bounded as two special cases. First, sufficient conditions are developed to ensure the unforced system to be regular, impulse-free, and exponentially mean-square stable. Then, by proposing a state feedback controller, sufficient conditions in terms of strict linear matrix inequalities are derived to guarantee the closed-loop system to be stochastically stabilziable. Finally, a numerical example is provided to show the effectiveness of the obtained results.

Stability and Stabilization for Singular Switching Semi-Markovian Jump Systems With Generally Uncertain Transition Rates

Event-triggered communication mechanism (ETCM) provides an efficient way to reduce unwanted network traffic. This article studies the co-design of an ETCM and an annular finite-time (AFT) $H_{\infty }$ filter for networked switched systems (NSSs). First, the AFT definition and ETCM are presented. Second, a set of mode-dependent average dwell-time (MADT) switching rules is given. By resorting to a delay-dependent Lyapunov functional approach, some feasible AFT $H_{\infty }$ filters are designed. Third, it is proved that the filtering error system (FES) has a good performance in attenuating the external disturbances. Finally, the feasibility of the developed method is verified via simulation.

Event-Triggered Communication and Annular Finite-Time H ∞ Filtering for Networked Switched Systems

Stability analysis of switched linear singular systems

In this paper, we consider the event-triggered control problem for continuous-time switched linear systems. It is assumed that only the sampled information of system state and switching signal is available to the controller at each sampling instant. Based on a mode-dependent event-triggered transmission scheme, the closed-loop system is modeled as a switched system with delayed state and augmented switching signal. Then, an exponential stability condition, characterized by the dwell time and average dwell time of the switching signal, is obtained. The condition presents an extension of the multiple Lyapunov functional method based stability analysis for sampled-data control of nonswitched system. Consequently, the design methods for state-feedback controller gains and event-triggered parameters are then formulated by the properly selected quadratic Lyapunov functional. The analysis results are significant and also lead to an important step to study the event-triggered control for switched system. Finally, based on the definition of event-trigger efficiency, the effectiveness and improvement of the proposed approach are illustrated by two numerical examples.

Event-Triggered Control of Continuous-Time Switched Linear Systems

Synchronization of chaotic Lur’e systems with quantized sampled-data controller

This paper addresses the stability problem for linear continuous-time Markovian switching singular systems. Considering the inherent state jump behavior at the switching instants, a necessary and sufficient condition of exponential stability in the mean square sense for the Markovian switching singular system is established in terms of linear matrix inequalities by means of a stochastic Lyapunov approach. Based on the obtained stability result, sufficient conditions of exponential stability in the mean square sense for the Markovian switching singular system with uncertain and partly unknown transition probability are presented. Numerical examples are presented to illustrate the effectiveness of the proposed approach.

Lei Zhou

Papers

Stability analysis of switched linear singular systems

Event-Triggered Control of Continuous-Time Switched Linear Systems

Synchronization of chaotic Lur’e systems with quantized sampled-data controller

New Results on Stability Analysis of Markovian Switching Singular Systems

Event-triggered H∞ filtering of continuous-time switched linear systems