On the Observation Analysis and Observer Design for a Class of Hybrid Continuous-Discrete Dynamic System

This chapter deals with observability conditions and state observer design for a class of hybrid systems whose the continuous part combines continuous and discrete dynamics. The main contribution of the work lies in the performed observability conditions for this class of systems and the design of a hybrid observer to reconstruct both continuous and discrete states starting only from the knowledge of a continuous output. Firstly, a high-order sliding mode based observer is used to estimate the continuous state and to generate a discrete output. Secondly, starting from this discrete output, a discrete state reconstructor is designed. An illustrative example is provided to show the efficiency of the proposed observer.

[1]  Noureddine Manamanni,et al.  State observer and observability conditions for a class of hybrid continuous-discrete dynamic system , 2007, 2007 46th IEEE Conference on Decision and Control.

[2]  Mamadou Mboup,et al.  Analyse et représentation de signaux transitoires : application à la compression, au débruitage et à la détection de ruptures , 2005 .

[3]  Maria Domenica Di Benedetto,et al.  Observability and observer‐based control of hybrid systems , 2009 .

[4]  Giorgio Battistelli,et al.  Active mode observability of switching linear systems , 2007, Autom..

[5]  G. Bornard,et al.  Observability for any u(t) of a class of nonlinear systems , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[6]  Andrea Balluchi,et al.  A hybrid observer for the driveline dynamics , 2001, 2001 European Control Conference (ECC).

[7]  Maria Domenica Di Benedetto,et al.  Observability of Internal Variables in Interconnected Switching Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[8]  Mohamed Djemai,et al.  Singularly perturbed method for the control design of a synchronous motor with its PWM inverter , 1995, Proceedings of International Conference on Control Applications.

[9]  R. Hirschorn.  Invertibility of multivariable nonlinear control systems , 1979 .

[10]  J. Gauthier,et al.  Observability for any of a class of nonlinear systems , 1981 .

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

[12]  J. Barbot,et al.  Nonlinear Observer for Autonomous Switching Systems with Jumps , 2007 .

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

[14]  Kevin Guelton,et al.  Robust pole placement controller design in LMI region for uncertain and disturbed switched systems , 2008 .

[15]  Magnus Egerstedt,et al.  An observer for linear systems with randomly-switching measurement equations , 2003, Proceedings of the 2003 American Control Conference, 2003..

[16]  Jean-Pierre Barbot,et al.  State and unknown input estimation for linear discrete-time systems , 2005 .

[17]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[18]  S. Pettersson,et al.  Hybrid system stability and robustness verification using linear matrix inequalities , 2002 .

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

[20]  Alberto Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 2000, IEEE Trans. Autom. Control..

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

[22]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

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

[24]  Maria Domenica Di Benedetto,et al.  Discrete state observability of hybrid systems , 2009 .