Simultaneous uniform disturbance rejection and decoupling for nonsquare linear time-dependent analytic systems using restricted state feedback

Abstract

In this paper, we consider, for the first time, the combined problem of uniform disturbance rejection and decoupling of nonsquare linear time-dependent analytic systems via restricted static state feedback. The problem is treated on the basis of an algebraic approach, whose main feature is that it reduces the problem to that of solving a homogeneous algebraic system of equations. On the basis of this fundamental system of equations, necessary and sufficient conditions of a simple algebraic nature are derived for the existence of a restricted static state-feedback controller that rejects the disturbances and simultaneously decouples the closed-loop system. Furthermore, simple expressions for a special admissible controller pair are derived analytically.