y-Stability and stabilization in the mean of discrete-time stochastic systems

1984 ◽  
Vol 40 (1) ◽  
pp. 149-160 ◽  
Author(s):  
YANNIS A. PHILLIS
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Stability And Stabilization ◽  
The Mean

scholarly journals Robust Quadratic Stabilizability and H∞ Control of Uncertain Linear Discrete-Time Stochastic Systems with State Delay

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Xiushan Jiang ◽  
Xuemin Tian ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Feedback Controllers ◽  
State Delay ◽  
Quadratic Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Theoretical Results

This paper mainly discusses the robust quadratic stability and stabilization of linear discrete-time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is, respectively, obtained for the stability and stabilizability of the considered system. Moreover, we design the robust H∞ state feedback controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H∞ controllable. A sufficient condition for the existence of the desired robust H∞ controller is obtained. Finally, an example with simulations is given to verify the effectiveness of our theoretical results.

scholarly journals H∞Enhanced Control Design of Discrete-Time Takagi-Sugeno State-Multiplicative Noisy Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
State Feedback Control ◽  
Control Law ◽  
State Control ◽  
Bounded Real Lemma ◽  
Quadratic Performance ◽  
The Mean ◽  
Takagi Sugeno

Design conditions for existence of theH∞state feedback control for Takagi-Sugeno fuzzy discrete-time stochastic systems with state-multiplicative noise, stabilizing the closed-loop in such way that the quadratic performance in the mean is satisfied, are presented in the paper. Using newly introduced enhanced form of the bounded real lemma for such stochastic systems, the LMI-based procedure is provided for computation of gain matrices of the state control law, realized in the parallel distributed compensation structure. The approach is illustrated on an example, demonstrating the validity of the proposed method.

scholarly journals Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shuang Liang ◽  
Yali Dong
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Stochastic Stabilization ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. By utilizing a new Lyapunov-Krasovskii functional and some well-known inequalities, some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (LMI). Then based on the state feedback controller, the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. The controller gain is designed to ensure the robust stochastic stability of the closed-loop system. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method.

Improved Delay-Dependent Robust Stability Criteria for Discrete-Time Stochastic Uncertain Networks with Time-Varying Delays

2012 ◽  
Vol 430-432 ◽  
pp. 849-852
Author(s):  
Meng Zhuo Luo ◽  
Shou Ming Zhong
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Time Varying ◽  
Mean Square ◽  
Stability Criteria ◽  
The Mean ◽  
Delay Dependent ◽  
Uncertain Networks ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

In this paper, the mean square asymptotical stability is investigated for a class of discrete-time stochastic systems with time-varying delays and norm-bounded uncertainties,a numerical example is presented to show the usefulness of the derived LMI-based stability condition.

scholarly journals Finite-time Stochastic Stability and Stabilization for Uncertain Discrete-time Stochastic Systems with Time-varying Delay

2021 ◽  
Vol 20 ◽  
pp. 244-251
Author(s):  
Xinyue Tang ◽  
Yali Dong ◽  
Meng Liu
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Finite Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
Time Varying Delay ◽  
Stability And Stabilization ◽  
Varying Delay

This paper deals with the problems of finite-time stochastic stability and stabilization for discrete-time stochastic systems with parametric uncertainties and time-varying delay. Using the Lyapunov-Krasovskii functional method, some sufficient conditions of finite-time stochastic stability for a class of discrete-time stochastic uncertain systems are established in term of matrix inequalities. Then, a new criterion is proposed to ensure the closed-loop system is finite-time stochastically stable. The controller gain is designed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

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