H2/H∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching

被引：7

作者：

Wang, Meijiao ^{[1
]}

Meng, Qingxin ^{[2
]}

Shen, Yang ^{[3
]}

机构：

[1] Univ Shanghai Sci & Technol, Sch Business, Shanghai 200093, Peoples R China

[2] Huzhou Univ, Dept Math Sci, Huzhou 313000, Zhejiang, Peoples R China

[3] Univ New South Wales, Sch Risk & Actuarial Studies, Sydney, NSW 2052, Australia

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2021年 / 34卷 / 03期

基金：

中国国家自然科学基金;

关键词：

H-2/H-infinity control; jump bounded real lemma; jump-diffusion systems; Markovian switching; system of Riccati type differential equations; H-INFINITY CONTROL; DISCRETE-TIME-SYSTEMS; STATE-FEEDBACK CONTROL; DIFFERENTIAL-EQUATIONS; ROBUST STABILIZATION; LINEAR-SYSTEMS; POISSON NOISE; STABILITY; DESIGN; DELAY;

D O I：

10.1007/s11424-020-9131-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a stochastic H-2/H-infinity control problem is investigated for Poisson jump-diffusion systems with Markovian switching, which are driven by a Brownian motion and a Poisson random measure with the system parameters modulated by a continuous-time finite-state Markov chain. A stochastic jump bounded real lemma is proved, which reveals that the norm of the perturbation operator below a given threshold is equivalent to the existence of a global solution to a parameterized system of Riccati type differential equations. This result enables the authors to obtain sufficient and necessary conditions for the existence of H-2/H-infinity control in terms of two sets of interconnected systems of Riccati type differential equations.

引用

页码：924 / 954

页数：31

共 42 条

[1] [Anonymous], 2010, MATH METHODS ROBUST
[2] Stochastic H2/H∞ control with state-dependent noise
Chen, BS
Zhang, WH
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (01) : 45 - 57
[3] Robust stabilization design for nonlinear stochastic system with Poisson noise via fuzzy interpolation method
Chen, Wen-Hao
Chen, Bor-Sen
[J]. FUZZY SETS AND SYSTEMS, 2013, 217 : 41 - 61
[4] Mixed H2/H∞-control of discrete-time Markovian jump linear systems
Costa, OLV
Marques, RP
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (01) : 95 - 100
[5] Mixed H2/H∞ control of hidden Markov jump systems
de Oliveira, A. M.
Costa, O. L. V.
[J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2018, 28 (04) : 1261 - 1280
[6] H state-feedback controller design for continuous-time nonhomogeneous Markov jump systems
Ding, Yucai
Liu, Hui
Shi, Kaibo
[J]. OPTIMAL CONTROL APPLICATIONS & METHODS, 2017, 38 (01) : 133 - 144
[7] STATE-SPACE SOLUTIONS TO STANDARD H-2 AND H-INFINITY CONTROL-PROBLEMS
DOYLE, JC
GLOVER, K
KHARGONEKAR, PP
FRANCIS, BA
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1989, 34 (08) : 831 - 847
[8] Systems of matrix rational differential equations arising in connection with linear stochastic systems with Markovian jumping
Dragan, V
Morozan, T
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 194 (01) : 1 - 38
[9] Stability and robust stabilization to linear stochastic systems described by differential equations with Markovian jumping and multiplicative white noise
Dragan, V
Morozan, T
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2002, 20 (01) : 33 - 92
[10] On an infinite dimensional perturbed Riccati differential equation arising in stochastic control
Fragoso, MD
Baczynski, J
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 406 : 165 - 176

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