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Research Papers

# Exponentially Dissipative Control for Singular Impulsive Dynamical Systems

[+] Author and Article Information
Li Yang

School of Mathematics,
Liaoning University,
Shenyang, Liaoning 110036, China
e-mail: yangli2923@163.com

Xinzhi Liu

Department of Applied Mathematics,
University of Waterloo,
e-mail: xzliu@uwaterloo.ca

Zhigang Zhang

Department of Statistics and
Applied Mathematics,
Hubei University of Economics,
Wuhan 430205, China
e-mail: zzg@hbue.edu.cn

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 14, 2013; final manuscript received October 25, 2016; published online February 9, 2017. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 139(4), 041008 (Feb 09, 2017) (6 pages) Paper No: DS-13-1446; doi: 10.1115/1.4035166 History: Received November 14, 2013; Revised October 25, 2016

## Abstract

This paper studies the problem of exponentially dissipative control for singular impulsive dynamical systems. Some necessary and sufficient conditions for exponential dissipativity of such systems are established in terms of linear matrix inequalities (LMIs). A state feedback controller is designed to make the closed-loop system exponentially dissipative. A numerical example is given to illustrate the feasibility of the method.

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## References

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## Figures

Fig. 2

The value of V(tk+)−V(tk)−rd(ωd(t),yd(t))≤0,( t=tk) for the system via the state feedback controller

Fig. 1

The value of V˙(t,x(t))+εV(x(t))−rc(ωc(t),yc(t))≤0,( t≠tk) for the system via the state feedback controller

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