Delay‐dependentrobust control of stochastic systems with convex polynomial uncertainty

Abstract

Summary This article addresses a robust control problem of time‐varying stochastic systems with time‐delays. Through Linear Parameter Varying (LPV) modeling approach, the time‐varying parameters can be described via the convex combination. Therefore, the LPV stochastic system is interpreted by a weighting function and multiplicative noised linear systems. Furthermore, stabilization problem for the systems is investigated via Gain‐Scheduled (GS) technique to increase robustness. For the problem, some sufficient conditions are derived by Integral Lyapunov‐Krasovskii Function (ILKF) such that the conservatism caused by derivative of weighting function is ignored. Besides, an Iterative Linear Matrix Inequality algorithm is used to determine the auxiliary variable such that the problem can be solved via the convex calculation. Finally, some simulations are provided to demonstrate effectiveness and applicability of this article.

A mesh‐based partitioning algorithm for decreasing conservatism in solving bilinear matrix inequality problems

“…One category of variables is considered to be fixed, and therefore, the whole problem becomes convex and solvable in the form of an LMI problem. The two‐step process and iterative LMI (ILMI), 28 29 can be considered as variations of this technique. As for drawbacks, the AM and ILMI methods were developed for specific cases and hence needed reformulation to be used in other instances.…”

Robust Decentralized Fuzzy Controller Design for Nonlinear Large-Scale Interconnected Descriptor Systems

“…Many works have proposed the T-S fuzzy control problem of different types of nonlinear systems. For example, the disturbance or timedelay have been considered by TSFM [2][3][4][5]. The stability conditions of the T-S fuzzy singular system provided in this paper are derived by the quadratic Lyapunov function [2].…”

Discrete‐time state‐feedback control of polytopic LPV systems

“…Over the past few decades, linear parameter-varying (LPV) control systems have been widely researched and the results applied to several practical applications. [1][2][3][4][5][6][7][8][9] The main reason is due to the ability to represent nonlinear systems in an LPV framework. 10 As a result, relevant conditions akin to those found for linear systems in general may be derived to assess the stability and performance of this system class.…”

“…[21][22][23][24] In order to cope with such descriptions, a set of linear matrix inequality-(LMI) based conditions was provided using a similar formulation given in Oliveira and Geromel 25 for time-varying parameters. This distinguished contribution has been successfully applied to several control problems such as gain-scheduled control, 5,26 model predictive control 27 and filter design. 18,28 The main advantage of the method consists in dealing with necessary and sufficient conditions and the possibility of recovering the quadratic stability approach as a particular case.…”