scholarly journals Robust Stability, Stabilization, andH∞Control of a Class of Nonlinear Discrete Time Stochastic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Tianliang Zhang ◽  
Yu-Hong Wang ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
State Control ◽  
Stochastic Stabilizability ◽  
Discrete Stochastic System

This paper studies robust stability, stabilization, andH∞control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robustH∞state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robustH∞performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.

scholarly journals Stabilization of discrete-time LTI positive systems

2017 ◽  
Vol 27 (4) ◽  
pp. 575-594 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Linear Matrix ◽  
Positive System ◽  
Matrix Inequalities ◽  
Positive Systems ◽  
Feedback Controllers ◽  
Associated Solutions ◽  
State Observers ◽  
Time Linear

AbstractThe paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

scholarly journals StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

scholarly journals Feedback Stabilization for a Class of Nonlinear Stochastic Systems with State- and Control-Dependent Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yu-Hong Wang ◽  
Tianliang Zhang ◽  
Weihai Zhang
Keyword(s):  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Global State ◽  
Nonlinear Stochastic Systems ◽  
Feedback Stabilizability ◽  
And Control

This paper mainly studies the state feedback stabilizability of a class of nonlinear stochastic systems with state- and control-dependent noise. Some sufficient conditions on local and global state feedback stabilizations are given in linear matrix inequalities (LMIs) and generalized algebraic Riccati equations (GAREs). Some obtained results improve the previous work.

scholarly journals New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
P. Niamsup ◽  
G. Rajchakit
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Polytopic Uncertainties ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Convex Polytopic Uncertainties ◽  
Robust Stability And Stabilization

This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results.

scholarly journals Robust Stability Criteria of Roesser-Type Discrete-Time Two-Dimensional Systems with Parameter Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yan Zhao ◽  
Tieyan Zhang ◽  
Dan Zhao ◽  
Fucai You ◽  
Miao Li
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
2D Systems ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Parameter Dependent

This paper is concerned with robust stability analysis of uncertain Roesser-type discrete-time two-dimensional (2D) systems. In particular, the underlying parameter uncertainties of system parameter matrices are assumed to belong to a convex bounded uncertain domain, which usually is named as the so-called polytopic uncertainty and appears typically in most practical systems. Robust stability criteria are proposed for verifying the robust asymptotical stability of the related uncertain Roesser-type discrete-time 2D systems in terms of linear matrix inequalities. Indeed, a parameter-dependent Lyapunov function is applied in the proof of our main result and thus the obtained robust stability criteria are less conservative than the existing ones. Finally, the effectiveness and applicability of the proposed approach are demonstrated by means of some numerical experiments.

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.

Passivity analysis and passification for a class of switched stochastic systems with time-varying delay

2013 ◽  
Vol 91 (12) ◽  
pp. 1049-1056 ◽  
Author(s):  
Huimei Jia ◽  
Zhengrong Xiang
Keyword(s):  
State Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Passivity Analysis ◽  
Switched Stochastic Systems ◽  
Delay Dependent ◽  
Varying Delay

This paper is concerned with the problems of passivity analysis and passification for a class of switched stochastic systems with time-varying delay. Firstly, based on the multiple storage functions approach, a delay-dependent sufficient condition for the underlying systems to be stochastically passive is derived in terms of linear matrix inequalities. Then, based on the obtained passivity condition, a state feedback passive controller is designed. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method.

scholarly journals LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
A. Hmamed ◽  
M. Alfidi ◽  
A. Benzaouia ◽  
F. Tadeo
Keyword(s):  
Lyapunov Function ◽  
Robust Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Polytopic Uncertainty ◽  
Matrix Inequalities ◽  
Discrete Time Systems ◽  
Parameter Dependent ◽  
Time Systems

Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.

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