A New Robust Pole Placement Stabilization for a Class of Time-Varying Polytopic Uncertain Switched Nonlinear Systems under Arbitrary Switching

Abstract

This paper is concerned with the problem of robust stabilization via state feedback control for a class of both
continuous and discrete-time switched nonlinear systems with polytopic time-varying uncertainty. These studied systems are
modeled by differentials or differences equations. Therefore, a transformation of the systems representation under the arrow
form is performed. Subsequently, by using a constructed common Lyapunov function and applying the Kotelyanski lemma
associated with the M ?matrix proprieties. A new robust pole placement stabilization is proposed. These obtained results
provide a solution to one of the basic problems for switched nonlinear systems which ensures asymptotic stability under
arbitrary switching. Compared with the existing results of uncertain switched nonlinear systems, these proposed conditions are
formulated in terms of the time-varying polytopic uncertain parameters and they allow us to avoid searching a common
Lyapunov function which is a difficult. Finally, a validation to stabilize a shunt DC motor with uncertain models under
variable mechanical loads is performed to illustrate the effectiveness of the theoretical results.