Sulikowski, Bartlomiej (Univ. of Zielona Gora), Galkowski, Krzysztof (Univ. of Zielona Góra), Datta, Biswa Nath (Northern Illinois Univ.), Bachelier, Olivier (The Univ. of Poitiers), Kummert, Anton (Univ. of Wuppertal,)

An LMI Technique for Stability and Stabilization of Discrete-Time Second-Order Control Systems

Scheduled for presentation during the Mini-Symposium "Multidimensional Systems – Circuits, Signals, and Control" (TuA11), Tuesday, July 25, 2006, 11:15−11:40, Room 104a

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 27, 2023

Abstract

This paper presents several new LMI results on stability, feedback stabilization and pole placement in several important regions of the complex plane, including an ellipse, for discrete-time second-order control systems. The results are derived via transformation of the second-order system to an equivalent first-order descriptor system, thus avoiding the necessity of inversion of a possible ill-conditioned leading coefficient matrix of the system. LMI results for the standard first-order state-space control problems are well established in the literature. However, the LMI techniques for secondorder discrete control problems are not developed at the same level. Our results in this paper are mainly of existence type; however, numerical examples have been provided using SIMULINK and other LMI softwares, establishing the validity of our results.