On Passivity of Networked Nonlinear Systems with Packet Drops

We analyze passivity for a class of discrete-time switched n onli ear systems that switch between two modes an uncontrolled mode in which the system evolves open loop, and a controlled mode in which a control input is applied to the system. Such a model has recently been used f or a network controlled system in the presence of packet drops introduced by a communication channel. For t he case when the open loop system is non-passive, classical passivity theory considers the switched system t o be non-passive as well. We give a new generalized definition of passivity for such a system and show that if the r atio of the time steps for which the system evolves open loop versus the time steps for which the system evolves c losed loop is bounded below a critical ratio, then the nonlinear system is locally passive in this sense. Moreo ver, we show that this generalized definition is useful since it preserves two important properties of the classica l passivity concept that passivity implies asymptotic stability for zero state detectable systems using feedback and that passivity is preserved in parallel and feedback interconnections.

[1]  Xiaofeng Wang,et al.  Event-Triggering in Distributed Networked Control Systems , 2011, IEEE Transactions on Automatic Control.

[2]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[3]  Anthony N. Michel,et al.  Relaxation of Hypotheses in LaSalle-Krasovskii-Type Invariance Results , 2011, SIAM J. Control. Optim..

[4]  Dragan Nesic,et al.  Input-output stability properties of networked control systems , 2004, IEEE Transactions on Automatic Control.

[5]  Enric Fossas,et al.  Feedback passivity of nonlinear discrete-time systems with direct input-output link, , 2004, Autom..

[6]  P. Olver.  Nonlinear Systems , 2013 .

[7]  P. Antsaklis,et al.  : Event-Triggered Real-Time Scheduling For Stabilization of Passive / Output Feedback Passive Systems Technical Report of the ISIS Group at the University of Notre Dame isis-2010-001 October , 2010 , 2010 .

[8]  Wei Lin,et al.  Losslessness, feedback equivalence, and the global stabilization of discrete-time nonlinear systems , 1994, IEEE Trans. Autom. Control..

[9]  Christopher I. Byrnes,et al.  Passivity and absolute stabilization of a class of discrete-time nonlinear systems, , 1995, Autom..

[10]  Passivity-Based Control Design for Cyber-Physical Systems , 2008 .

[11]  James Lam,et al.  Stabilization of linear systems over networks with bounded packet loss , 2007, Autom..

[12]  Jun Zhao,et al.  Dissipativity Theory for Switched Systems , 2005, CDC 2005.

[13]  J. Baillieul,et al.  Challenges in Networked Real-Time Systems , 2009 .

[14]  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).

[15]  Ricardo G. Sanfelice,et al.  Passivity-based controllers for a class of hybrid systems with applications to mechanical systems interacting with their environment , 2011, IEEE Conference on Decision and Control and European Control Conference.

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

[17]  Long Wang,et al.  An LMI approach to networked control systems with data packet dropout and transmission delays , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[18]  Jun Zhao,et al.  Dissipativity Theory for Switched Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[19]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[20]  Panos J. Antsaklis,et al.  Control and Communication Challenges in Networked Real-Time Systems , 2007, Proceedings of the IEEE.

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

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

[23]  Panos J. Antsaklis,et al.  Passivity Analysis for Discrete-Time Periodically Controlled Nonlinear Systems , 2012 .

[24]  Navarro López,et al.  Dissipativity and passivity-related properties in nonlinear discrete-time systems , 2002 .

[25]  Panos J. Antsaklis,et al.  Event-triggered real-time scheduling for stabilization of passive and output feedback passive systems , 2011, Proceedings of the 2011 American Control Conference.