Robust Stabilization Approach and H_∞ Performance via Static Output Feedback for a Class of Nonlinear Systems

Abstract

This paper deals with the stability and stabilization problems for a class of discrete-time nonlinear systems. The systems are composed of a linear constant part perturbated by an additive nonlinear function which satisfies a quadratic constraint. A new approach to design a static output feedback controller is proposed. A sufficient condition, formulated as an LMI optimization convex problem, is developed. In fact, the approach is based on a family of LMI parameterized by a scalar, offering an additional degree of freedom. The problem of performance taking into account an H ∞ criterion is also investigated. Numerical examples are provided to illustrate the effectiveness of the proposed conditions.

An improved output feedback decentrilized control approaches for interconnected large scale systems

“…For this reason, we introduce some transformations to simplify the Kso fC G term of the inequality (14) by using (15) With this transformation the optimization problem given by (14) is equivalent to the one defined in theorem 2 .•…”

“…There are many control results concerning linear nominal systems with linear subsystem interconnections or interconnections satisfying linear bounds [10]. The early works were based on Lyapunov methods [1][2][3][4] and [15]. However, the stability results of the composite system are much dependent on the choice of the Lyapunov functions of the subsystems.…”

“…However, the stability results of the composite system are much dependent on the choice of the Lyapunov functions of the subsystems. Furthermore, in some papers the design of discrete static or dynamic output controllers has attracted attention [1][2][3][4], [15] and [17]. Notice that the dynamic output feedback control can be formulated as a static output feedback (SOF).…”

“…In this paper, we present a new approach to SOF synthesis for the large scale interconnected systems. Indeed, it is a sufficient condition for robust stabilization, in terms of LMI and based on the introduction of a relaxation variable like in [15]. This technique allows a decoupling between the Lyapunov matrix and the SOF gain.…”

Static output feedback control for LPV systems under affine uncertainty structure

“…Our approach is formulated in terms of Parameter Dependent Linear Matrix Inequalities (PDLMIs) , with a single line search parameter α. The synthesis of static output feedback control for the closed loop system is based indeed on a method that uses the singular value decomposition , inspired from [18], [19]. The way we resolve the issue, is proved to be less conservative than some others given in the literature as those of [10] or [11].…”