Controller Based Observer in Switched System with Norm Bounded Uncertainty

Maher Maher

doi:10.3844/ajassp.2012.1008.1013

Abstract

Problem statement: This study discusses the robust stabilization of n orm bounded discrete switched systems. Approach: The proposed method is using the second Lyapunov approach and the poly-quadratic function concept. The stabilization conditions are written through linear matrix inequality relations. The control law is based on a static output feedback with the use of a switched observer. The synthesis conditions of the controlle r are written in the form of linear matrix inequali ties difficult to resolve by current numerical solvers. That's why relaxations are proposed to mitigate the pessimism of LMI conditions obtained. Results: The poly-quadratic Lyapunov approach provides a constructive way to tackle uncertainty in the switc hed framework. The feasibility is illustrated by th e example of discrete uncertain switched systems. Conclusion: With these results, the study of stability can be achieved for arbitrary switching laws, state -dependent, time dependent or generated by a controller. However, the implementation of the cont rol law is possible only if the switching status is well known in real time.

Highlights

Many natural and artificial systems work in Morse, 2002) which operating constraints require different operating modes, each with its own dynamic. switching between multiple controllers
Switched systems are hybrid systems system (1) where each subsystem is vitiated by a norm defined by a set whose elements are dynamic bounded uncertainty (Maherzi et al, 2007; Zhou and continuous and/or discrete time models with Khargonekar, 1987; 1988), this system can be described commutation law which define, in time, the jumps by the following equalities (1): between the elements, leading to a non stationary dynamic system
Relatively non restrictive compared to the quadratic approach) stability condition for discrete switched With Eq 2 and 3: systems is provided using the poly-quadratic approach recently proposed by (Daafouz and Bernussou, 2001) △Al = DlFl El to analyze stability and stabilization control of Linear

Summary

INTRODUCTION

Many natural and artificial systems work in Morse, 2002) which operating constraints require different operating modes, each with its own dynamic. This study proposes an extension of this works in with every change of speed, the human heart switches the case when the switches are made between uncertain between different modes depending on the emotional LTI systems. The control investigated is of state feedback state of the person. These systems concoct continuous control, observer based and dynamic controller. Dynamics with both synchronous or asynchronous discrete events. Such class of systems is called hybrid

MATERIALS AND METHODS

RESULTS

DISCUSSION

CONCLUSION