Observer Design for Discrete-Time Switching Nonlinear Models

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. Zs. Lendek (B) · P. Raica Department of Automation, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania e-mail: [email protected] P. Raica e-mail: [email protected] J. Lauber · T.M. Guerra University of Valenciennes and Hainaut-Cambresis, LAMIH UMR CNRS 8201, Le Mont Houy, 59313 Valenciennes Cedex 9, France e-mail: [email protected] T.M. Guerra e-mail: [email protected] © Springer International Publishing Switzerland 2015 M. Djemai and M. Defoort (eds.), Hybrid Dynamical Systems, Lecture Notes in Control and Information Sciences 457, DOI 10.1007/978-3-319-10795-0_2 27 28 Zs. Lendek et al.