Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasvskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method,

Operator Jensen's Inequality on C*-algebras

A real continuous function which is defined on an interval is said to beA-convex if it is convex on the set of self-adjoint elements,with spectra in the interval,in all matrix algebras of the unital C-algebra A.We give a general formation of Jensen’s inequality for A-convex functions.

Stochastic synchronization of neutral-type chaotic impulse neural networks with leakage delay and Markovian jumping parameters

Purpose-The purpose of this paper is to develop a methodology for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.Design/methodology/approach-The authors perform drive-response concept and time-delay feedback control techniques to investigate a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.New sufficient criterion is established without strict conditions imposed on the activation functions.Findings-It turns out that the approach results in new sufficient criterion easy to be verified but without the usual assumption of the differentiability and monotonicity of the activation functions.Two examples show the effectiveness of the obtained results.Originality/value-The novelty of the proposed approach lies in removing the usual assumption of the differentiability and monotonicity of the activation functions,and the use of the Lyapunov functionalmethod,Jensen integral inequality,a novel Gu’s lemma,reciprocal convex and linear convex combination technique for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.