Reliable regulation in centralized control systems subject to polynomial exogenous signals

This paper addresses the design of a reliable control system for a linear, asymptotically stable plant. Specifically, the considered problem consists of finding a compensator which, besides guaranteeing closed loop asymptotic stability and zero error regulation when all the instrumentation is in operation, also ensures that these properties are preserved, at their maximum possible extent, when some sensors and/or actuators failures occur, that is, some of the feedback loops open. Thus, a single regulator has to be found, able to contemporarily solve a certain number of classical regulator problems. Referring to exogenous signals polynomial in time and a centralized control structure, the paper shows that a solution exists if and only if each standard regulator problem, composing the overall reliable regulator problem, admits a solution.