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 H ∞ controller design for linear neutral systems with discrete and distributed delays

This article considers the delay-dependent H _∞ control problem for linear neutral systems with both discrete and distributed delays. The problem we address is to design a state feedback controller such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed H _∞ performance level. First, a delay-dependent sufficient condition for the solvability of the problem is obtained in terms of matrix inequalities. Then, by using the cone complementarity linearization approach, an H _∞ controller is developed based on the solvability condition. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Reduced-order filtering design for non-linear systems with H ∞ setting

In this article, sufficient conditions are presented for the existence of an H ^∞ filter with a state dimension less than the plant. The conditions are characterised in terms of the solution to a Hamilton–Jacobi inequality, which is exactly the one used in the construction of the full-order H ^∞ filters. When these conditions hold, state-space formulae are also given for such reduced-order filters. Both affine and general non-affine non-linear systems are examined. The development uses only elementary concepts of dissipativity and differential game, thus the given proofs are simple and clear. To illustrate our result, some numerical examples are also included.     

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.     

Robust H∞ control of uncertain stochastic Markovian jump systems with mixed time-varying delays

In this paper, robust H_∞ control for a class of uncertain stochastic Markovian jump systems (SMJSs) with interval and distributed time-varying delays is investigated. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By employing the Lyapunov-Krasovskii functional and stochastic analysis theory, some novel sufficient conditions in terms of linear matrix inequalities are derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results.     

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.     

Adaptive robust H ∞ filter design for linear systems with time-varying uncertainty

This article studies the problem of designing robust H _∞ filters for linear uncertain systems. The uncertainty parameters are assumed to be time-varying, unknown, but bounded, which appear affinely in the matrices of system models. An adaptive mechanism is introduced to construct novel filters with variable gains, which can reduce the conservativeness of the traditional robust H _∞ filters. The proposed adaptive filter design conditions are given in terms of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed strategy.     

Novel compensation-based non-fragile H ∞ control for uncertain neutral systems with time-varying delays

This article studies the non-fragile H _∞ control problem for a class of uncertain linear neutral systems with time-varying delays, where the delay in neutral-type term includes a fast-varying case (i.e. the derivative of delay is more than one), which is seldom considered in current literature. The less conservative delay-dependent H _∞ control results for this systems are proposed by applying a new Lyapunov–Krasovskii functional and a geometric series compensation method. Based on the new functional, the systems with fast-varying neutral-type delay can be handled. The benefit brought by applying the compensation method is that many more useful elements can be included in criteria, which are generally ignored when estimating the upper bound of the derivative of Lyapunov–Krasovskii functional. A numerical example is provided to verify the effectiveness of the proposed criteria.     

H ∞ filtering for nonlinear singular Markovian jumping systems with interval time-varying delays

The problem of H _∞ filtering for nonlinear singular Markovian jumping systems with interval time-varying delays is investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Furthermore, the derivative of the time-varying delay function can be larger than one. With partial knowledge of the jump rates of the Markov process, a new delay-range-dependent bounded real lemma for the solvability of the jump system is obtained based on the Lyapunov–Krasovskii functional, which is in terms of strict linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired H _∞ filter is given. Numerical examples are given to illustrate the effectiveness of the developed techniques.     

Exponential stability and robust H∞ control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

This paper deals with stability and robust H_∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H_∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.     

H ∞ filtering for stochastic systems with time-varying delay

This article considers the problem of H _∞ filter design for stochastic systems with time-varying delay. The time delay is assumed to be of interval type. Attention is focused on the design of delay-dependent filters that guarantee the asymptotic stability in mean square and a prescribed noise attenuation level in an H _∞ sense for the filtering error dynamics. The delay-dependent H _∞ filter design scheme is proposed in terms of a linear matrix inequality. A numerical example is used to illustrate the effectiveness of the proposed approach.     

Improved H ∞ analysis of Markovian jumping stochastic systems with time-varying delays

This article investigates the problems of H _∞ analysis for Markovian jump stochastic systems with both nonlinear disturbance and time-varying delays. By virtue of the delay partition approach, the improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian jump stochastic systems are obtained in terms of linear matrix inequalities (LMIs). The proposed approach involves neither free weighting matrices nor any model transformation, and it is shown that the new criteria have the capability of providing less conservative results than the state-of-the-art. Two numerical simulations are conducted to demonstrate the effectiveness of the proposed method in comparison with existing methods.     

H ∞ fault detection filter design for linear discrete-time systems with multiple time delays

This paper deals with the design of H^∞ fault detection filters for discrete-time systems with multiple time delays, in which total decoupling of the fault effects from unknown inputs, including model uncertainties and external plant disturbances, is impossible. Through the appropriate choice of the filter gain, the filter is convergent if there is no fault in the system, and the effect of disturbances on the residual is minimized in the sense of H^∞ norm. The problem of achieving satisfactory sensitivity of the residual to faults is formulated and its solution given. The detection threshold associated with the filter is also discussed. Finally, a wind tunnel example illustrates the efficiency of the proposed method.     

Fuzzy robust H ∞ filter design for nonlinear discrete-time systems with interval time delays

This article deals with the problem of H _∞ filter design for nonlinear discrete-time systems with norm-bounded parameter uncertainties and time-varying delays. A new Lyapunov function and free-weighting matrix method are used for filtering design, consequently, a delay-dependent design method is first proposed in terms of linear matrix inequalities, which produces a less conservative result. Finally, numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.