Mode-dependent robust and non-fragile finite-time H∞ control for nonlinear singular Markovian jump systems

2021 ◽  
pp. 014233122110350
Author(s):  
Hongping Niu ◽  
Lin Li ◽  
Pengnan Wang
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Controller ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Closed Loop Systems ◽  
Singular Markovian Jump Systems ◽  
Finite Time Boundedness ◽  
Jump Systems

This paper is concerned with the problem of mode-dependent robust and non-fragile finite-time [Formula: see text] control for a class of nonlinear singular Markovian jump systems (NSMJSs) with parameter uncertainties and time-varying norm-bounded disturbance. Some sufficient conditions ensuring the singular stochastic [Formula: see text] finite-time boundedness (SS[Formula: see text]FTB) are developed for the given system by using the stochastic analysis and linear matrix inequality techniques. Then, a finite-time [Formula: see text] state feedback controller is designed, which can guarantee the [Formula: see text] finite-time boundedness of the closed-loop systems. Furthermore, a robust and non-fragile finite-time [Formula: see text] state feedback controller is also provided to ensure the [Formula: see text] finite-time boundedness of the closed-loop systems when the controller gain has an additive perturbation. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

scholarly journals Finite-TimeH∞Filtering for Singular Stochastic Markovian Jump Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Yan ◽  
Xiaojia Zhou ◽  
Jun Cheng ◽  
Fangnian Lang
Keyword(s):  
Finite Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Time Interval ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Finite Time Boundedness ◽  
Jump Systems

The issue of finite-timeH∞filtering for singular stochastic Markovian jump systems with time-varying delays is concerned in this paper.H∞filtering is designed for underlying closed-loop singular Markovian jump system and system state does not exceed a given bound over some finite-time interval. Considering the full information of underlying Markov process, sufficient conditions are obtained to guarantee that the described system is finite-time stability andH∞filtering finite-time boundedness. By establishing the results of stochastic character and finite-time boundedness, the closed-loop singular Markovian jump system trajectory stays within the given bound. At last, a numerical example is supplied to show the efficiency of the proposed method.

scholarly journals Finite-Time Control for Markovian Jump Systems with Polytopic Uncertain Transition Description and Actuator Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhongyi Tang
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Actuator Saturation ◽  
Feedback Controller ◽  
Markovian Jump Systems ◽  
Time Interval ◽  
Markovian Jump ◽  
State Feedback Controller ◽  
Attenuation Level ◽  
Jump Systems

The problem of finite-timeL2-L∞control for Markovian jump systems (MJS) is investigated. The systems considered time-varying delays, actuator saturation, and polytopic uncertain transition description. The purpose of this paper is to design a state feedback controller such that the system is finite-time bounded (FTB) and a prescribedL2-L∞disturbance attenuation level during a specified time interval is guaranteed. Based on the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design the delayed feedback controller which satisfies the given attenuation level. Finally, illustrative examples show that the proposed conditions are effective for the design of robust state feedback controller.

scholarly journals Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yucai Ding ◽  
Hui Liu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Reachable Set ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
State Feedback Controller ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

The problems of reachable set estimation and state-feedback controller design are investigated for singular Markovian jump systems with bounded input disturbances. Based on the Lyapunov approach, several new sufficient conditions on state reachable set and output reachable set are derived to ensure the existence of ellipsoids that bound the system states and output, respectively. Moreover, a state-feedback controller is also designed based on the estimated reachable set. The derived sufficient conditions are expressed in terms of linear matrix inequalities. The effectiveness of the proposed results is illustrated by numerical examples.

scholarly journals Observer-Based Finite-TimeH∞Control of Singular Markovian Jump Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Yingqi Zhang ◽  
Wei Cheng ◽  
Xiaowu Mu ◽  
Xiulan Guo
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Feasibility Problem ◽  
Auxiliary Result ◽  
Markovian Jump ◽  
Singular Markovian Jump Systems ◽  
Finite Time Stabilization ◽  
Jump Systems

This paper addresses the problem of finite-timeH∞control via observer-based state feedback for a family of singular Markovian jump systems (SMJSs) with time-varying norm-bounded disturbance. Firstly, the concepts of singular stochastic finite-time boundedness and singular stochastic finite-timeH∞stabilization via observer-based state feedback are given. Then an observer-based state feedback controller is designed to ensure singular stochastic finite-timeH∞stabilization via observer-based state feedback of the resulting closed-loop error dynamic SMJS. Sufficient criteria are presented for the solvability of the problem, which can be reduced to a feasibility problem involving linear matrix inequalities with a fixed parameter. As an auxiliary result, we also discuss the problem of finite-time stabilization via observer-based state feedback of a class of SMJSs and give sufficient conditions of singular stochastic finite-time stabilization via observer-based state feedback for the class of SMJSs. Finally, illustrative examples are given to demonstrate the validity of the proposed techniques.

scholarly journals Robust Finite-TimeH∞Control for Nonlinear Markovian Jump Systems with Time Delay under Partially Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Dong Yang ◽  
Guangdeng Zong
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
State Feedback ◽  
Transition Probabilities ◽  
Feedback Stabilization ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Finite Time Boundedness ◽  
Jump Systems ◽  
Nonlinear Markovian Jump Systems

This paper is concerned with the problem of robust finite-timeH∞control for a class of nonlinear Markovian jump systems with time delay under partially known transition probabilities. Firstly, for the nominal nonlinear Markovian jump systems, sufficient conditions are proposed to ensure finite-time boundedness,H∞finite-time boundedness, and finite-timeH∞state feedback stabilization, respectively. Then, a robust finite-timeH∞state feedback controller is designed, which, for all admissible uncertainties, guarantees theH∞finite-time boundedness of the corresponding closed-loop system. All the conditions are presented in terms of strict linear matrix inequalities. Finally a numerical example is provided to demonstrate the effectiveness of all the results.

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