Passivity Analysis and Passification of Discrete-Time Hybrid Systems

For discrete-time hybrid systems in piecewise affine or piece-wise polynomial (PWP) form, this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or PWP storage functions. By exploiting linear matrix inequality techniques and sum of squares decomposition methods, passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages, providing a tool particularly important for stability of interconnected heterogeneous dynamical systems.

[1]  M. Kanat Camlibel,et al.  On Linear Passive Complementarity Systems , 2002, Eur. J. Control.

[2]  Stephen P. Boyd,et al.  Quadratic stabilization and control of piecewise-linear systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[3]  P. Moylan,et al.  Connections between finite-gain and asymptotic stability , 1980 .

[4]  L. Chua.  Passivity and complexity , 1999 .

[5]  Manfred Morari,et al.  A Generalized Approach for Analysis and Control of Discrete-Time Piecewise Affine and Hybrid Systems , 2001, HSCC.

[6]  Randy A. Freeman,et al.  Guaranteed stability of haptic systems with nonlinear virtual environments , 2000, IEEE Trans. Robotics Autom..

[7]  P. Parrilo.  Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[8]  Arjan van der Schaft,et al.  A novel theory for sampled data system passivity , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[9]  Alberto Bemporad,et al.  Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form , 2004, IEEE Transactions on Automatic Control.

[10]  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).

[11]  J. Edward Colgate,et al.  Passivity of a class of sampled-data systems: Application to haptic interfaces , 1997 .

[12]  A. Papachristodoulou,et al.  Analysis of switched and hybrid systems - beyond piecewise quadratic methods , 2003, Proceedings of the 2003 American Control Conference, 2003..

[13]  Bernhard Maschke,et al.  Dissipative Systems Analysis and Control , 2000 .

[14]  Alberto Bemporad,et al.  Optimization-Based Verification and Stability Characterization of Piecewise Affine and Hybrid Systems , 2000, HSCC.

[15]  Alberto Bemporad,et al.  PASSIVITY ANALYSIS AND PASSIFICATION OF DISCRETE-TIME HYBRID SYSTEMS , 2005 .

[16]  J. Edward Colgate,et al.  Passivity of a class of sampled-data systems: Application to haptic interfaces , 1997, J. Field Robotics.

[17]  M. Jirstrand,et al.  On stability and passivity of a class of hybrid systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[18]  Randy A. Freeman,et al.  On the role of dissipation in haptic systems , 2004, IEEE Trans. Robotics.

[19]  有本 卓,et al.  Control theory of non-linear mechanical systems : a passivity-based and circuit-theoretic approach , 1996 .

[20]  Anders Rantzer,et al.  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1997, 1997 European Control Conference (ECC).

[21]  Eduardo Sontag.  Nonlinear regulation: The piecewise linear approach , 1981 .

[22]  S. Pettersson,et al.  Stability and robustness for hybrid systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

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

[24]  Domenico Prattichizzo,et al.  Multirate analysis of haptic interaction stability with deformable objects , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[25]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

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

[27]  A. Bemporad,et al.  Passivity analysis of discrete-time hybrid systems using piecewise polynomial storage functions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[28]  M. Morari,et al.  Stability and stabilization of piecewise affine and hybrid systems: an LMI approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).