scholarly journals Exponential Admissibility and Dynamic Output Feedback Control of Switched Singular Systems with Interval Time-Varying Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Jinxing Lin ◽  
Chunxia Fan
Keyword(s):  
Output Feedback ◽  
Singular Systems ◽  
Delay System ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Dynamic Output ◽  
Varying Delay

This paper is concerned with the problems of exponential admissibility and dynamic output feedback (DOF) control for a class of continuous-time switched singular systems with interval time-varying delay. A full-order, dynamic, synchronously switched DOF controller is considered. First, by using the average dwell time approach, a delay-range-dependent exponential admissibility criterion for the unforced switched singular time-delay system is established in terms of linear matrix inequalities (LMIs). Then, based on this criterion, a sufficient condition on the existence of a desired DOF controller, which guarantees that the closed-loop system is regular, impulse free and exponentially stable, is proposed by employing the LMI technique. Finally, some illustrative examples are given to show the effectiveness of the proposed approach.

scholarly journals Non-fragile dynamic output feedback H∞ control for a class of uncertain switched systems with time-varying delay

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Yuning Song ◽  
Yuzhong Liu
Keyword(s):  
Output Feedback ◽  
Linear Matrix ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Dynamic Output ◽  
Nonlinear Matrix Inequality ◽  
Nonlinear Matrix ◽  
Varying Delay

The problem of non-fragile dynamic output feedback H∞ control for a class of uncertain switched systems with time-varying delay is discussed. Firstly, the form of non-fragile dynamic output feedback H∞ controller is given. Under the condition that the upper bound of time delay and the upper bound of delay derivative are limited simultaneously, Lyapunov functional and its corresponding switching rules are constructed by using single Lyapunov function method and convex combination technique; Secondly, we use the inequality lemma to scale the derived Lyapunov functional in order to eliminate the time-varying delay term in the inequality, and then introduce the J-function to obtain a nonlinear matrix inequality that satisfies the H∞ performance index γ, we also employ Schur complement lemma to transform the nonlinear matrix inequality into set of linear matrix inequalities consisting of two linear matrix inequalities, a sufficient condition for the existence of a non-fragile dynamic output feedback H∞ controller and satisfying the H∞ performance index γ is concluded for a class of uncertain switching systems with variable time delay; Finally, a switched system composed of two subsystems is considered and the effectiveness and practicability of the theorem are illustrated by numerical simulation with LMI toolbox. 

scholarly journals Dynamic Output Feedback Passive Control of Uncertain Switched Stochastic Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Huimei Jia ◽  
Hamid Reza Karimi ◽  
Zhengrong Xiang
Keyword(s):  
Output Feedback ◽  
Passive Control ◽  
Stochastic Systems ◽  
Sufficient Condition ◽  
Dynamic Output Feedback ◽  
Time Varying ◽  
Time Varying Delay ◽  
Switched Stochastic Systems ◽  
Dynamic Output ◽  
Varying Delay

This paper is concerned with the issues of passivity analysis and dynamic output feedback (DOF) passive control for uncertain switched stochastic systems with time-varying delay via multiple storage functions (MSFs) method. Firstly, based on the MSFs method, a sufficient condition for the existence of the passivity of the underlying system is established in terms of linear matrix inequalities (LMIs). Furthermore, the problem of dynamic output feedback passive control is investigated. Based on the obtained passivity condition, a sufficient condition for the existence of the desired switched passive controller is derived. Finally, a numerical example is presented to show the effectiveness of the proposed method.

scholarly journals Delay-Dependent Stability Criteria for Singular Systems with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Jianmin Jiao
Keyword(s):  
Singular Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
Decision Variables ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with stability analysis for singular systems with interval time-varying delay. By constructing a novel Lyapunov functional combined with reciprocally convex approach and linear matrix inequality (LMI) technique, improved delay-dependent stability criteria for the considered systems to be regular, impulse free, and stable are established. The developed results have advantages over some previous ones as they involve fewer decision variables yet less conservatism. Numerical examples are provided to demonstrate the effectiveness of the proposed stability results.

scholarly journals Observer-based controller design of time-delay systems with an interval time-varying delay

2012 ◽  
Vol 22 (4) ◽  
pp. 921-927 ◽  
Author(s):  
Mai Viet Thuan ◽  
Vu Ngoc Phat ◽  
Hieu Trinh
Keyword(s):  
Output Feedback ◽  
Design Procedure ◽  
Feedback Controller ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Output Feedback Controller ◽  
Varying Delay

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

scholarly journals Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Interval Time ◽  
Delay Function ◽  
Time Varying Delay ◽  
Bounded Nonlinearity ◽  
Varying Delay

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

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