New Results on the Multi-Controller Scheme for the Reliable Control of Linear Plants

In this paper we present some new results on the control of linear plants using two simultaneously acting controllers. First we tackle the problem of reliable stabilization using a multiple controller configuration, where the objective is to find two controllers that stabilize a given system both when acting together or when acting independently. Secondly, we consider the problem of reliable control where we seek conditions under which a nominal controller can be decomposed into a pair of controllers that together solve the reliable stabilization problem. This is a simple way to incorporate passive redundancy into the system, thus enhancing the reliability of the control system. We present necessary and sufficient conditions for the solution of the reliable stabilization problem. In case of the reliable control problem we give a necessary ard sufficient condition for its solution when one or both of the controllers is assumed to be stable. In addition, we show at certain technical constraints on the decomposition restrict the level of performance achievable following a component failure. This is illustrated, together with the decomposition process, for an aircraft design example.