Wide-area damping controller for randomly varying delay: a dynamic output feedback approach

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.

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

Mathematical Problems in Engineering ◽

10.1155/2013/281747 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 2

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.

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

Mathematical Problems in Engineering ◽

10.1155/2010/680382 ◽

2010 ◽

Vol 2010 ◽

pp. 1-21 ◽

Cited By ~ 5

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.

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