Dissipativity of hybrid systems: Feedback interconnections and networks

This paper focuses on the notions of QSR dissipativity and passivity in hybrid systems. The work presented in this paper can mainly be divided into two parts- (i) feedback and parallel interconnections and, (ii) networks. First, it is shown that the negative feedback interconnection of two QSR dissipative hybrid systems is QSR dissipative. Also, passivity is preserved when passive hybrid systems are connected in parallel. It is also shown that QSR dissipativity and hence passivity are closely related to the stability of hybrid systems. In the second part of this work, passivity of networked hybrid input-output automata, in presence of network delays is studied. The issues of both the constant and time varying delays is addressed using a wave variable transform based approach.

[1]  M. Zefran,et al.  A notion of passivity for hybrid systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[2]  Peter L. Lee,et al.  Process Control: The Passive Systems Approach , 2010 .

[3]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[4]  Yue Wang,et al.  Control of cyberphysical systems using passivity and dissipativity based methods , 2013, Eur. J. Control.

[5]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[6]  Wassim M. Haddad,et al.  Nonlinear impulsive dynamical systems. I. Stability and dissipativity , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[7]  Ricardo G. Sanfelice,et al.  Interconnections of Hybrid Systems : Some Challenges and Recent Results , 2011 .

[8]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[9]  Jean-Jacques E. Slotine,et al.  Stable Adaptive Teleoperation , 1990, 1990 American Control Conference.

[10]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[11]  A. Michel,et al.  Lyapunov Stability of a Class of Discrete Event Systems , 1991 .

[12]  Mark W. Spong,et al.  Bilateral Teleoperation Over Unreliable Communication Networks , 2008, IEEE Transactions on Control Systems Technology.

[13]  Nancy A. Lynch,et al.  Hybrid I/O automata , 1995, Inf. Comput..

[14]  A. S. Vincentelli,et al.  Handbook of Hybrid Systems Control: Theory, Tools, Applications , 2011 .

[15]  Wassim M. Haddad,et al.  Non-linear impulsive dynamical systems. Part I: Stability and dissipativity , 2001 .

[16]  Michael J. McCourt,et al.  Dissipativity theory for hybrid systems with applications to networked control systems , 2013 .

[17]  Panos J. Antsaklis,et al.  Stability of networked passive switched systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[18]  Arjan van der Schaft,et al.  An Introduction to Hybrid Dynamical Systems, Springer Lecture Notes in Control and Information Sciences 251 , 1999 .

[19]  M.W. Spong,et al.  Output Synchronization of Nonlinear Systems with Time Delay in Communication , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.