Exact differentiation via sliding mode observer for switched Systems

Abstract The main topic of this paper is the problem of observer synthesis for switched systems, which includes, as a specific case, the design of observers based on high order sliding mode technique. High order sliding mode is used to overcome the occurring chattering phenomena which induces some irrelevant decision of switching between the subsystems when the trajectory is in the neighborhood of the switching manifold. Moreover, in this paper, after presenting the general structure of the step by step differentiator, well show the step by step finite time convergence of the estimation error and the discrete state estimation. Two simulation examples illustrate the efficiency of the proposed approach.

[1]  J. Barbot,et al.  Sliding mode observer for triangular input form , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[2]  Eduardo Sontag.  On the Observability of Polynomial Systems. , 1977 .

[3]  Driss Boutat,et al.  About the observability of piecewise dynamical systems , 2004 .

[4]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

[5]  E. Sontag,et al.  Generalized Controller Canonical Forms for Linear and Nonlinear Dynamics , 1990 .

[6]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[7]  Noureddine Manamanni,et al.  SLIDING MODE OBSERVER FOR TRIANGULAR INPUT HYBRID SYSTEM , 2005 .

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

[9]  S. Drakunov.  Sliding-mode observers based on equivalent control method , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

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

[11]  Michel Fliess,et al.  Generalized controller canonical form for linear and nonlinear dynamics , 1990 .

[12]  Anthony N. Michel,et al.  Stability analysis of discontinuous dynamical systems determined by semigroups , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[14]  Arie Levant,et al.  Higher order sliding modes as a natural phenomenon in control theory , 1996 .

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

[16]  S. Pettersson.  Observer Design for Switched Systems using Multiple Quadratic Lyapunov Functions , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[17]  Daniel Liberzon,et al.  On stabilization of linear systems with limited information , 2003, IEEE Trans. Autom. Control..

[18]  Eliathamby Ambikairajah,et al.  A hybrid state estimation scheme for power systems , 2002, Asia-Pacific Conference on Circuits and Systems.

[19]  Mohamed Djemai,et al.  Sliding Mode Observers , 2002 .

[20]  M. De la Sen,et al.  Design of linear observers for a class of linear hybrid systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[21]  Maria Domenica Di Benedetto,et al.  DIGITAL IDLE SPEED CONTROL OF AUTOMOTIVE ENGINES USING HYBRID MODELS , 2005 .