Observer and Observer-Based Control Designs with Guaranteed Performance for Linear Discrete-Time Descriptor Systems

Lázaro Ismael Hardy Llins; Daniel Coutinho; Carlos E. de Souza

doi:10.20906/CBA2022/3672

Lázaro Ismael Hardy Llins SESI – Innovation Center for Health Technologies, CISTS/FIESC, Rod. Admar Gonzaga 2765, Florianópolis, SC 88034-001
Daniel Coutinho Department of Automation and Systems (DAS), Universidade Federal de Santa Catarina (UFSC), Florianópolis, SC, 88040-900
Carlos E. de Souza Department of Mathematical and Computational Methods, Laboratório Nacional de Computação Científica (LNCC/MCTI), Petrópolis, 25651-075

DOI: https://doi.org/10.20906/CBA2022/3672

Keywords: Descriptor system, State observer, Linear Matrix Inequalities (LMIs), Separation Principle

Abstract

This paper approaches the problem of Luenberger-like observer design for a class of LTI discrete- time descriptor systems. We present and prove sufficient conditions for the observer design with a guaranteed decay rate where the admissible descriptor systems. In addition, assuming some standard controllability properties, a separation principle is demonstrated considering an observer-based output feedback control law. The observer design is also extended to cope with model disturbances in an H2 sense. The effectiveness of the proposed methodology is illustrated by numerical examples.