Algebraic switching time identification for a class of linear hybrid systems

Abstract In this paper, a method for the finite time estimation of the switching times in linear switched systems is proposed. The approach is based on distribution theory. Switching time estimates are given by explicit algebraic formulae that can be implemented in a straightforward manner using standard tools from computational mathematics. Simulations illustrate the proposed techniques.

[1]  Alessandro Pisano,et al.  Finite-time observation of the continuous and discrete state for a class of nonlinear switched dynamics , 2009, ADHS.

[2]  G. Zhai,et al.  Quadratic stabilizability of switched linear systems with polytopic uncertainties , 2003 .

[3]  Daniel Liberzon,et al.  Common Lyapunov functions for families of commuting nonlinear systems , 2005, Syst. Control. Lett..

[4]  C. Fantuzzi,et al.  Identification of piecewise affine models in noisy environment , 2002 .

[5]  Angelo Alessandri,et al.  Design of Luenberger Observers for a Class of Hybrid Linear Systems , 2001, HSCC.

[6]  U. Boscain.  Stability of planar switched systems: the linear single, input case , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[7]  Yasmin L. Hashambhoy,et al.  Recursive Identification of Switched ARX Models with Unknown Number of Models and Unknown Orders , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[8]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

[9]  Michel Fliess,et al.  Parameters estimation of systems with delayed and structured entries , 2009, Autom..

[10]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[11]  A. Stephen Morse,et al.  Supervisory control with state-dependent dwell-time logic and constraints , 2004, Autom..

[12]  Noureddine Manamanni,et al.  Exact differentiation and sliding mode observers for switched Lagrangian systems , 2006 .

[13]  José Ragot,et al.  Switching systems: active mode recognition, identification of the switching law , 2007 .

[14]  Ugo Boscain,et al.  Stability of planar nonlinear switched systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  George J. Pappas,et al.  Observability of Switched Linear Systems in Continuous Time , 2005, HSCC.

[16]  Cédric Join,et al.  Robust residual generation for linear fault diagnosis: an algebraic setting with examples , 2004 .

[17]  Jean-Pierre Barbot,et al.  An algebraic framework for the design of nonlinear observers with unknown inputs , 2007, 2007 46th IEEE Conference on Decision and Control.

[18]  G. A. Ackerson,et al.  On state estimation in switching environments , 1968 .

[19]  Wilfrid Perruquetti,et al.  Fast state estimation in linear time-varying systems: An algebraic approach , 2008, 2008 47th IEEE Conference on Decision and Control.

[20]  Yang Tian,et al.  Fast state estimation in linear time-invariant systems: an algebraic approach , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[21]  L. Schwartz.  Théorie des distributions , 1966 .

[22]  Jong Myung Rhee,et al.  Issues of Fail-Over Switching for Fault-Tolerant Ethernet Implementation , 2009, 2009 International Conference on New Trends in Information and Service Science.

[23]  Shuzhi Sam Ge,et al.  Controllability and reachability criteria for switched linear systems , 2002, Autom..

[24]  Hebertt Sira-Ramírez,et al.  Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques , 2007 .

[25]  M. Fliess,et al.  An algebraic framework for linear identification , 2003 .

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

[27]  Raymond A. DeCarlo,et al.  Switched Controller Synthesis for the Quadratic Stabilisation of a Pair of Unstable Linear Systems , 1998, Eur. J. Control.

[28]  Alberto L. Sangiovanni-Vincentelli,et al.  Design of Observers for Hybrid Systems , 2002, HSCC.

[29]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[30]  Romain Bourdais,et al.  Stabilization of nonlinear switched systems using control Lyapunov functions , 2007 .

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

[32]  E. De Santis,et al.  On observability and detectability of continuous-time linear switching systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[33]  S. Shankar Sastry,et al.  Observability of Linear Hybrid Systems , 2003, HSCC.

[34]  J. L. Mancilla-Aguilar,et al.  A converse Lyapunov theorem for nonlinear switched systems , 2000 .

[35]  B. Carlsson.  Recursive identification , 2010 .

[36]  Michel Fliess,et al.  On-line identification of systems with delayed inputs , 2006 .

[37]  Guangming Xie,et al.  Controllability of switched linear systems , 2002, IEEE Trans. Autom. Control..

[38]  Alessandro Giua,et al.  Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems , 2011 .

[39]  Eduardo D. Sontag,et al.  A polynomial-time algorithm for checking equivalence under certain semiring congruences motivated by the state-space isomorphism problem for hybrid systems , 2001, Theor. Comput. Sci..

[40]  Yi Ma,et al.  Identification of hybrid linear time-invariant systems via subspace embedding and segmentation (SES) , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[41]  Wilfrid Perruquetti,et al.  Real-time estimation for switched linear systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[42]  Daniel Liberzon,et al.  Lie-Algebraic Stability Criteria for Switched Systems , 2001, SIAM J. Control. Optim..

[43]  Romain Bourdais,et al.  TOWARDS A MODEL-FREE OUTPUT TRACKING OF SWITCHED NONLINEAR SYSTEMS , 2007 .

[44]  J. Rudolph,et al.  An algebraic approach to parameter identification in linear infinite dimensional systems , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[45]  R. Balasubramanian.  Design of observers , 1989 .

[46]  René Vidal,et al.  Identification of Hybrid Systems: A Tutorial , 2007, Eur. J. Control.