H ∞ output-feedback control for switched linear discrete-time systems with time-varying delays

In this paper, the problem of H _∞ output feedback control for switched linear discrete-time systems with time delays is investigated. The time delay is assumed to be time-varying and bounded. By constructing a switched quadratic Lyapunov function for the underlying system, both static and dynamic H _∞ output feedback controllers are designed respectively such that the corresponding closed-loop system under arbitrary switching signals is asymptotically stable and a prescribed H _∞ noise-attenuation level bound is guaranteed. A cone complementary linearization algorithm is exploited to design the controllers. A numerical example is presented to show the effectiveness of the developed theoretical results.     

Delay-dependent robust stabilization and H ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.     

Memoryless H ∞ controller design for switched non-linear systems with mixed time-varying delays

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.     

Robust H ∞ filter design of uncertain T-S fuzzy neutral systems with time-varying delays

This article addresses the problem of robust H _∞ filter design of a class of Takagi–Sugeno fuzzy neutral systems with time-varying delays and norm-bounded parameter uncertainties. A fuzzy filter is constructed, which ensures both the robust stability and a prescribed H _∞ performance of the filtering error system. A linear matrix inequality approach is developed, and a delay-dependent sufficient condition is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed approach.     

Delay-dependent robust H-infinity control for discrete-time uncertain systems with time-varying state delays

1 Introduction The analysis and synthesis of dynamic control systems with time delays is a subject of great practical and theo- retical importance, and has received considerable attention for decades (see [1,2] and references therein). Stability cri- teria can be classified roughly into two categories: delay- independent and delay-dependent [3]. Delay-independent criteria contains no information on the delay size, which, as might be expected, is generally conservative, especially when the dela…     

Fault tolerant H ∞ control for a class of polynomial non-linear discrete-time systems

This paper studies the fault tolerant control (FTC) problem for a class of polynomial nonlinear discrete-time systems with guaranteed H _∞ performance in the presence of actuator faults. The concerned fault is considered as a multi-model of the typical aberration in actuators’ effectiveness. A quadratic-like polynomial Lyapunov function is presented for the H _∞ specification. The main contribution of this paper is that the effect of the nonlinear terms appear in FTC analysis is described as an index in order to transform the controller design into a semi-definite programming (SDP). A numerical example is given to verify the applicability of this new approach for the nonlinear FTC synthesis.     

Decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays

This article considers the decentralised H _∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H _∞ filter is designed for each subsystem. It is shown that the stability with H _∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach.     

Passivity and H∞ control of switched discrete-time nonlinear systems using linearisation

Local passivity and H_∞ control of switched discrete-time nonlinear systems are studied using the linearisation technique in this paper. We first establish LMI-based sufficient conditions under which theconsidered system is locally strictly QSR-dissipative. Then, two special cases of QSR-dissipativity, local passivity and l₂ gain, are investigated. In view of the derived conditions being all convex in linearised system matrices, local feedback passification and H_∞ control problems of switched discrete-time nonlinear systems are solved. The efficiency of the proposed method is verified through numerical examples.     

Reliable H∞ guaranteed cost control for uncertain switched fuzzy stochastic systems with multiple time-varying delays and intermittent actuator and sensor faults

Neural Computing and Applications - In this paper, the issue of delay-dependent passive fault-tolerant control and optimal guaranteed cost control is considered for multiple time-varying delayed...     

Robust H∞ performance for discrete time T-S fuzzy switched memristive stochasticneural networks with mixed time-varying delays

ABSTRACT

In this paper, we study the robust H _∞ performance for discrete-time T-S fuzzy switched memristive stochastic neural networks with mixed time-varying delays and switching signal design. The neural network under consideration is subject to time-varying and norm bounded parameter uncertainties. Decomposing of the delay interval approach is employed in both the discrete delays and distributed delays. By constructing a proper Lyapunov-Krasovskii functional (LKF) with triple summation terms and using an improved summation inequality techniques. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee the considered discrete-time neural networks to be exponentially stable. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the developed theoretical results.     

Quantized robust ℋ∞ control of discrete-time systems with random communication delays

The article considers stability and robust ?_∞ controller design of discrete-time systems with random communication delays and state quantization. A finite state Markov process is used to model communication delays between sensors and controllers. Measurements are assumed to be quantized by a logarithmic quantizer, and the effect of quantization errors are incorporated into the controller design. Based on a Lyapunov–Krasovskii approach, novel methodologies for analysing stability and designing a time-delay mode-dependent quantized state feedback controller are proposed. The controller is obtained through solving bilinear matrix inequalities (BMIs) using the cone complementarity linearisation algorithm.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

Delay-dependent H ∞ control of linear discrete-time systems with an interval-like time-varying delay

The free-weighting-matrix approach is developed to study the H _∞ control of linear discrete-time systems with an interval-like time-varying delay. First, a delay- and range-dependent criterion for a given H _∞ performance is derived. Second, a memoryless H _∞ state-feedback controller is designed based on a performance analysis. Finally, two numerical examples demonstrate the effectiveness of the proposed method and show that both the upper bound and range of an interval-like time-varying delay affect the stability and/or H _∞ performance of a system.     

Conjugation and H ∞ control of discrete-time systems

We establish conjugation notion in discrete-time systems, first introduced into the H ^∞ control theory of continuous-time systems by Kimura (1989). In discrete-time systems, conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle. With the aid of J-lossless conjugation conjugation by a J.lossless system), it is shown that the parametrization of sub-optimal solutions of H ^∞ model-matching problems is reduced to a Lyapunov-type equation. The parametrization of all solutions is given in an extremely simple way. It is further proved that the J-lossless conjugation of the H ^∞ model-matching problem is a natural state-space representation of classical interpolation in discrete-time systems.     

Exponential stability of switched systems with impulsive effect

The exponential stability of a class of switched systems containing stable and unstable subsystems with impulsive effect is analyzed by using the matrix measure concept and the average dwell-time approach. It is shown that if appropriately a large amount of the average dwell-time and the ratio of the total activation time of the subsystems with negative matrix measure to the total activation time of the subsystems with nonnegative matrix measure is chosen, the exponential stability of a desired degree is guaranteed. Using the proposed switching scheme, we studied the robust exponential stability for a class of switched systems with impulsive effect and structure perturbations. Simulations validate the main results.