Switching time estimation for linear switched systems: an algebraic approach

This paper aims at estimating the switching time for linear switched systems, i.e. the time instant when a sub-model is switched on while another one is switched off. Assuming that the state of the active sub-models is known, a distribution point of view is adopted to get a real-time estimation of these switching times. Real-time means that an explicit algorithm computes on-line these time instants in a fast and efficient way. Simulations illustrate the proposed techniques which is easily implementable.

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

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

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

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

[5]  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).

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

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

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

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

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

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

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

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

[14]  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.

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

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

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

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

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

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

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

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

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

[24]  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.

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

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

[29]  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).

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

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