Synthesis of Reliable Control Systems Based on Simultaneous Stabilization Problem in a Behavioral Framework

A Parameterization of the Simultaneous Stabilizers for Simultaneously Stabilizable Pairs

Abstract

In this paper, we address synthesis of reliable control systems based on simultaneous stabilization problem in a behavioral framework. Firstly, we provide a necessary and sufficient condition for a control law to stabilize given two plants simultaneously. Nextly, by using this condition, we give a parameterization of all of the simultaneous stabilizing controllers for given two plants. By focusing on the single-input single-output case, we also give a condition that enables us to check whether given two plants are simultanously stabilizable in terms of poles and zeros of the transfer functions, which is a generalization of the results obtained in the standard system theory. Moreover, we give an illustrative example in order to show the validity of our results.