Observer Design for Discrete-Time Switching Nonlinear Models

Zsofia Lendek , Paula Raica , Jimmy Lauber (1) , Thierry-Marie Guerra (1)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201

Switched systems are often described by continuous and discrete dynamics as well as their interactions. Although results are available for linear switching systems, for nonlinear switching models few results exist. In this chapter, we consider observer design for discrete-time switching nonlinear systems with a Takagi–Sugeno representation. For designing the observers, a switching nonquadratic Lyapunov function is used. Such Lyapunov functions have shown a real improvement of the design conditions for discrete-time Takagi–Sugeno models. The Lypunov function can be defined for each subsystem or just for the moments when switching takes place. In the first case the results are more general, but also more conservative. The second case represents a significant improvement for periodic models. Thanks to the Lyapunov function used, it is possible to design observers for some switching systems with unobservable subsystems. The developed conditions are formulated as linear or bilinear matrix inequalities. Their advantages and shortcomings are illustrated on numerical examples.

Mots clés: Discrete-time Switching; Nonquadratic Lyapunov Functions; Switched Linear Systems; Lypunov Function; Switching Law

Domaines: Automatique / Robotique

Zsofia Lendek, Paula Raica, Jimmy Lauber, Thierry-Marie Guerra. Observer Design for Discrete-Time Switching Nonlinear Models. Defoort & Djemaï. Hybrid Dynamical Systems, 457, Springer International Publishing, pp.27-58, 2015, Lecture Notes in Control and Information Sciences, ⟨10.1007/978-3-319-10795-0_2⟩. ⟨hal-03406825⟩