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,
Waterloo, ON N2L 3G1, Canada
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

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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Chellaboina, V. , and Haddad, W. , 2003, “ Exponentially Dissipative Nonlinear Dynamical Systems: A Nonlinear Extension of Strict Positive Realness,” Math. Probl. Eng., 2003(1), pp. 25–45. [CrossRef]
Anderson, B. , 1972, “ The Small-Gain Theorem, the Passivity Theorem and Their Equivalence,” J. Franklin Inst., 293(2), pp. 105–115. [CrossRef]
Joshi, S. , and Gupta, S. , 1996, “ On a Class of Marginally Stable Positive-Real Systems,” IEEE Trans. Autom. Control, 41(1), pp. 152–155. [CrossRef]
Hill, D. , and Moylan, P. , 1977, “ Stability Results for Nonlinear Feedback Systems,” Automatica, 13(4), pp. 377–382. [CrossRef]
Willems, J. , 1972, “ Dissipative Dynamical Systems Part I: General Theory,” Arch. Ration. Mech. Anal., 45(5), pp. 321–351. [CrossRef]
Dai, L. , 1989, Singular Control Systems, Springer-Verlag, Berlin/Heidelberg, Germany.
Wang, C. , 1996, “ State Feedback Impulse Elimination of Linear Time-Varying Singular Systems,” Automatica, 32(1), pp. 133–136. [CrossRef]
Wu, Z. , Lam, J. , Su, H. , and Chu, J. , 2012, “ Stability and Dissipativity Analysis of Static Neural Networks With Time Delay,” IEEE Trans. Neural Networks Learn. Syst., 23(2), pp. 199–210. [CrossRef]
Hill, D. , and Moylan, P. , 1980, “ Dissipative Dynamical Systems: Basic Input-Output and State Properties,” J. Franklin Inst., 309(5), pp. 327–357. [CrossRef]
Wang, C. , and Liao, H. , 2001, “ Impulse Observability and Impulse Controllability of Linear Time-Varying Singular Systems,” Automatica, 37(11), pp. 1867–1872. [CrossRef]
Haddad, W. , Chellaboina, V. , and Kablar, N. , 2001, “ Nonlinear Impulsive Dynamical Systems. Part I: Stability and Dissipativity,” Int. J. Control, 74(17), pp. 1631–1658. [CrossRef]
Ye, H. , Michel, A. , and Hou, L. , 1998, “ Stability Theory for HybridDynamical Systems,” IEEE Trans. Autom. Control, 43(4), pp. 461–474. [CrossRef]
Shen, J. , and Jing, Z. , 2006, “ Stability Analysis for Systems With Impulse Effects,” Int. J. Theor. Phys., 45(9), pp. 1703–1717. [CrossRef]
Liu, B. , Liu, X. , and Liao, X. , 2003, “ Robust Dissipativity for Uncertain Impulsive Dynamical Systems,” Math. Probl. Eng., 2003(3), pp. 119–128. [CrossRef]
Yang, L. , Liu, X. , and Zhang, Z. , 2012, “ Dissipative Control for Singular Impulsive Dynamical Systems,” Electron. J. Qual. Theory Differ. Equations, 2012(32), pp. 1–11. [CrossRef]
Yang, L. , Liu, X. , and Zhang, Z. , 2011, “ Dissipative Control for Discrete Singular Impulsive Dynamical Systems,” Proceedings of the 30th Chinese Control Conference, IEEE, pp. 203–207.
Boyd, S. E. , Ghaoui, L. , Feron, E. , and Balakrishnan, V. , 1994, Linear Matrix Inequalities in System and Control Theory, Society for Industrial Mathematics, Philadelphia, PA.


Grahic Jump Location
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

Grahic Jump Location
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




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