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 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.

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-Time Stabilization for Discrete-Time Delayed Markovian Jump Systems with Partially Delayed Actuator Saturation

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Guoliang Wang ◽  
Bo Feng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Controller Design ◽  
Actuator Saturation ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Time Control ◽  
Jump Systems

The finite-time control problem of discrete-time delayed Markovian jump systems with partially delayed actuator saturation is considered by a mode-dependent parameter approach. Different from the traditionally saturated actuators, a kind of saturated actuator being partially delay-dependent is firstly proposed, where both nondelay and delay states are included and occur asynchronously. Moreover, the probability distributions of such two terms are described by the Bernoulli variable and are taken into account in the controller design. Sufficient conditions for the existence of the desired controller are presented with LMIs. Finally, a numerical example is provided to show the effectiveness and superiority of the obtained results.

Finite-time H∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities

2013 ◽  
Vol 91 (12) ◽  
pp. 1020-1028 ◽  
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Guihua Li
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Partial Information ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Partly Unknown Transition Probabilities ◽  
Stability And Stabilization ◽  
Jump Systems

This paper addresses the problems of finite-time stochastic stability and stabilization for linear Markovian jump systems subject to partial information on the transition probabilities. By introducing bounded finite time and stochastic character, sufficient conditions that can ensure bounded finite time and H∞ finite-time bounded filtering are derived. Finally, an example is given to illustrate the efficiency of the proposed method.

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.

Sign in / Sign up

Export Citation Format

Share Document