$H_{\infty}$ FEEDBACK CONTROLS BASED ON DISCRETE-TIME STATE OBSERVATIONS FOR SINGULAR HYBRID SYSTEMS WITH NONHOMOGENEOUS MARKOVIAN JUMP

Zhiyong Ye; Suying Pan; Jin Zhou

doi:10.11948/20180315

2019 Volume 9 Issue 5

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Zhiyong Ye, Suying Pan, Jin Zhou. $H_{\infty}$ FEEDBACK CONTROLS BASED ON DISCRETE-TIME STATE OBSERVATIONS FOR SINGULAR HYBRID SYSTEMS WITH NONHOMOGENEOUS MARKOVIAN JUMP[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1750-1768. doi: 10.11948/20180315

Citation:

Zhiyong Ye, Suying Pan, Jin Zhou. $H_{\infty}$ FEEDBACK CONTROLS BASED ON DISCRETE-TIME STATE OBSERVATIONS FOR SINGULAR HYBRID SYSTEMS WITH NONHOMOGENEOUS MARKOVIAN JUMP[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1750-1768. doi: 10.11948/20180315

$H_{\infty}$ FEEDBACK CONTROLS BASED ON DISCRETE-TIME STATE OBSERVATIONS FOR SINGULAR HYBRID SYSTEMS WITH NONHOMOGENEOUS MARKOVIAN JUMP

1.
Institute of Applied Mathematics and Mechanics and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, 200072 Shanghai, China
2.
School of Science, Chongqing University of Technology, 400054 Chongqing, China

Corresponding author: Email address: yezhiyong1966@163.com(Z. Ye)

Abstract

Abstract

In this paper, the $H_{\infty}$-control problem for singular Markovian jump systems (SMJSs) with variable transition rates by feedback controls based on discrete-time state observations is studied. The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant. By designing a feedback controller based on discrete-time state observations, employing a stochastic Lyapunov-Krasovskii functional, and combining with the linear matrix inequalities (LMIs) technologies, sufficient conditions under the case of nonhomogeneous transition rates are developed such that the controlled system is regular, impulse free, and stochastically stable. Subsequently, the upper bound on the duration $\tau$ between two consecutive state observations and prescribed $H_{\infty}$ performance $\gamma$ are derived. Moreover, the achieved results can be easily checked by the Matlab LMI Tool Box. Finally, two numerical examples are presented to show the effectiveness of the proposed methods.
- Discrete-time state observation /
- stochastically stable /
- $H_{\infty}$feedback control /
- nonhomogeneous Markovian jump /
- singular system
MSC: 34D20, 34F05, 93D15

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