Estabilidade e estabilização de uma classe de sistemas não-lineares sujeitos a saturação

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

2012

RESUMO

This work addresses the problem of stability analysis and stabilization of nonlinear rational systems subject to saturation. The approach used in this study is based on the differential algebraic representation (DAR) of rational systems and on a modified version of the generalized sector condition to deal with saturation. First, methods to characterize the stability of discrete-time systems subject to disturbances are proposed. In this context, approaches based on linear matrix inequalities to compute estimates of the region of attraction of the system, as well as limits for a class of admissible ¿2 disturbances to ensure bounded trajectories and estimates of the ¿2-gain of the system are presented. Two approaches are considered: the first one based on a single quadratic Lyapunov function and the second one considering piecewise quadratic Lyapunov functions. Then, techniques for the synthesis of anti-windup compensators are proposed in order to enlarge the region of attraction of continuous-time systems. The conditions are developed and incorporated into an iterative algorithm, where at each iteration, a convex optimization problem with LMI constraints is solved. These results are extended to deal with uncertain systems and systems subject to disturbances. In order to avoid iterative methods and facilitate the application to multivariable systems, a new approach to synthesize this type of compensator (directly in terms of LMI) is proposed. Extensions of the results are also presented to deal with discrete-time systems. Finally, a method for the synthesis of static state feedback gains is proposed. This method is based on local stabilization conditions which allow to calculate the state feedback gain and a Lyapunov function leading to a maximized estimate of the region of attraction of the closed-loop system. The extension of these results for the case of discrete-time systems is also addressed. Numerical examples are presented in order to illustrate the application and to verify the efficiency of the proposed methods.

ASSUNTO(S)

disturbances stability anti-windup lmi sistemas nao lineares rational systems saturation feedback lyapunov functions nonlinear systems controle automático : estabilidade

ACESSO AO ARTIGO

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