scholarly journals H∞ Control for Nonlinear Infinite Markov Jump Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yueying Liu ◽  
Ting Hou
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Infinite Horizon ◽  
Mean Square ◽  
State Control ◽  
Markov Jump ◽  
Nonlinear Stochastic Systems ◽  
Markov Jump Systems ◽  
Jump Systems ◽  
Infinite State

In this paper, we discuss the infinite horizon H∞ control problem for a class of nonlinear stochastic systems with state, control, and disturbance dependent noise. The jumping parameters are modelled as an infinite-state Markov chain. Based on the solvability of a set of coupled Hamilton-Jacobi inequalities (HJIs), the exponential mean square H∞ controller for the considered nonlinear stochastic systems is obtained. A numerical example is given to show the effectiveness of the proposed design method.

scholarly journals Nonlinear StochasticH∞Control with Markov Jumps and(x,u,v)-Dependent Noise: Finite and Infinite Horizon Cases

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Li Sheng ◽  
Meijun Zhu ◽  
Weihai Zhang ◽  
Yuhong Wang
Keyword(s):  
Design Method ◽  
External Disturbance ◽  
Infinite Horizon ◽  
State Control ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Numerical Examples ◽  
Inequality Techniques ◽  
Jump Systems ◽  
Control Designs

This paper is concerned with theH∞control problem for nonlinear stochastic Markov jump systems with state, control, and external disturbance-dependent noise. By means of inequality techniques and coupled Hamilton-Jacobi inequalities, both finite and infinite horizonH∞control designs of such systems are developed. Two numerical examples are provided to illustrate the effectiveness of the proposed design method.

scholarly journals H∞Control for Nonlinear Stochastic Systems with Time-Delay and Multiplicative Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Ming Gao ◽  
Weihai Zhang ◽  
Zhengmao Zhu
Keyword(s):  
Time Delay ◽  
General Class ◽  
Multiplicative Noise ◽  
Stochastic Systems ◽  
Design Method ◽  
Infinite Horizon ◽  
Control Design ◽  
Mean Square ◽  
Nonlinear Stochastic Systems ◽  
Numerical Examples

This paper studies the infinite horizonH∞control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean squareH∞control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.

An event-triggered approach to finite-time observer-based control for Markov jump systems with repeated scalar nonlinearities

2017 ◽  
Vol 40 (9) ◽  
pp. 2789-2797 ◽  
Author(s):  
Jingyu Li ◽  
Liang Shen ◽  
Fengqi Yao ◽  
Huanyu Zhao ◽  
Jing Wang
Keyword(s):  
Finite Time ◽  
Design Method ◽  
Function Technique ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Diagonally Dominant Matrix ◽  
Error System ◽  
Dominant Matrix ◽  
Jump Systems ◽  
Event Triggered

This paper studies the issue of finite-time observer-based control via an event-triggered scheme for Markov jump repeated scalar nonlinear systems. An observer-based controller via an event-triggered scheme is proposed, which can save the limited network communication bandwidth effectively, so that the resulting error system is stochastically finite-time bounded. Based on the positive definite diagonally dominant matrix and the Lyapunov function technique, a sufficient condition is presented for the solvability of the addressed problem, and the desired observer-based controller can be constructed via a convex optimization problem. In the end, a simulation example is employed to show the validity and practicability of the proposed design method.

scholarly journals Spectral Perspective on the Stability of Discrete-Time Markov Jump Systems with Multiplicative Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ting Hou ◽  
Weihai Zhang ◽  
Hongji Ma
Keyword(s):  
Discrete Time ◽  
Multiplicative Noise ◽  
Mean Square ◽  
Critical Stability ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Mean Square Stability ◽  
Lyapunov Operator ◽  
The Stability ◽  
Jump Systems

We apply the spectrum analysis approach to address the stability of discrete-time Markov jump systems with state-multiplicative noise. In terms of the spectral distribution of a generalized Lyapunov operator, spectral criteria are presented to testify three different kinds of stochastic stabilities: asymptotic mean square stability, critical stability, and essential instability.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

2021 ◽  
pp. 014233122199096
Author(s):  
Yunling Shi ◽  
Xiuyan Peng
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Design Method ◽  
Transition Rates ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Reduced Order ◽  
Jump Systems ◽  
Stochastic Admissibility ◽  
Fault Detection Filters

This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.

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