A passivation method for the design of switched controllers

We consider a feedback switched control system with non-passive subsystems. Introducing a passivation matrix, we transform each non-passive subsystem into a passive one and investigate the passivity of the resulting closed-loop system. The results are further extended to input feedforward passive (IFP) and output feedforward passive (OFP) switched controllers. In addition, we construct a control framework to maintain passivity for switched systems and provide a numerical example to illustrate the accuracy of the results based on the system performance. Our theoretical framework can have important implications in the design of switched controllers based on the concept of passivity.

[1]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[2]  Patrizio Colaneri,et al.  Passivity of switched linear systems: Analysis and control design , 2012, Syst. Control. Lett..

[3]  Panos J. Antsaklis,et al.  Passivity indices and passivation of systems with application to systems with input/output delay , 2014, 53rd IEEE Conference on Decision and Control.

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

[5]  Jun Zhao,et al.  Passivity and stability of switched systems: A multiple storage function method , 2008, Syst. Control. Lett..

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

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

[8]  Sandra Hirche,et al.  Human-Oriented Control for Haptic Teleoperation , 2012, Proceedings of the IEEE.

[9]  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).

[10]  Jun Zhao,et al.  Passivity and feedback passification of switched discrete-time linear systems , 2013, Syst. Control. Lett..

[11]  L. Vu,et al.  Stability of interconnected switched systems and supervisory control of time-varying plants , 2007, 2007 46th IEEE Conference on Decision and Control.

[12]  Diana Bohm,et al.  L2 Gain And Passivity Techniques In Nonlinear Control , 2016 .

[13]  M. Branicky.  Stability of switched and hybrid systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  A. Morse,et al.  Stability of switched systems: a Lie-algebraic condition ( , 1999 .

[15]  Lihua Xie,et al.  Passivity analysis and passification for uncertain signal processing systems , 1998, IEEE Trans. Signal Process..

[16]  João Pedro Hespanha,et al.  Root-mean-square gains of switched linear systems , 2003, IEEE Trans. Autom. Control..

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

[18]  Georgi M. Dimirovski,et al.  Feedback passivation of switched nonlinear systems using storage-like functions , 2011 .

[19]  David J. Hill,et al.  Passivity-based control and synchronization of general complex dynamical networks , 2009, Autom..

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

[21]  M. Mahmoud,et al.  Passivity and passification of time-delay systems , 2004 .

[22]  Guang-Hong Yang,et al.  Passivity and output feedback passification of switched continuous-time systems with a dwell time constraint , 2015 .

[23]  Mehrdad Saif,et al.  PASSIVITY AND PASSIVITY BASED CONTROLLER DESIGN OF A CLASS OF SWITCHED CONTROL SYSTEMS , 2005 .

[24]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[25]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..