New H _∞ observer‐based control for delayed LPV stochastic system

Abstract

An H∞ observer‐based control problem of delayed Linear Parameter Varying (LPV) stochastic system is addressed in this paper. In the LPV stochastic system, stochastic behaviors and external disturbance in real environment are respectively described by stochastic difference function. Furthermore, the delay effects on state and control input are considered as time‐varying case for wide application. For the control problem, a lemma dealing with the delay terms is proposed to increase some slack variables. Based on the proposed lemma and the chosen Lyapunov‐Krasovskii function, some sufficient conditions are derived to relax the conservatism of stability criterion. Besides, disturbance effect on state and estimation error is constrained via H∞ performance for improving transient response. Through using the extended projection lemma, the derived conditions are formulated as strict Linear Matrix Inequality (LMI) problem. To avoid the potential oscillation, another lemma is proposed to separately assign the performance level during solving the conditions. All feasible solutions can be directly obtained by convex optimization algorithm without using extra calculation. Therefore, an observer‐based controller is established to guarantee the asymptotical stability and H∞ performance in the mean square. Finally, some numerical simulations are provided to demonstrate the effectiveness and applicability of the proposed method.

Passive Stabilization of Static Output Feedback of Disturbed Nonlinear Stochastic System

“…Comparing with ( 13) and ( 32), the solutions are obviously realized in (24) satisfying condition (13) in Theorem 1. The proof of Theorem 2 is completed.…”

“…In [20,21], a stochastic differential equation was proposed to describe stochastic systems. The works in the literature [22][23][24] have discussed the control problems of stochastic systems. A nonlinear stochastic system represented by the T-S fuzzy model was widely applied to discuss their stability analysis and controller synthesis.…”

“…On the other hand, the root-mean-square concept is always applied to discuss the stability of stochastic systems because of their unpredictability [22]. Moreover, the Itô formula [24] is required to manifest the unpredicted energy caused by stochastic behavior and to analyze the time-derivative trend. Furthermore, the attenuation of the T-S fuzzy model with multiplicative noise was investigated by [25,26] for achieving passivity.…”

A grid‐based searching algorithm for observer‐based multiobjective control of T–S fuzzy stochastic jump‐diffusion systems

“…Most controller design problems have focused on optimal solutions for one preferred performance index [1][2][3][4][5][6][7][8]. However, in practice, controllers usually require the ability to concurrently achieve multiple performance indices that often conflict.…”