Fixed order multivariable discrete-time control

In this paper we develop a new algorithm to compute stabilizing sets for a fixed order digital controller for a multivariable plant. This computation is crucial in applications and few results are available. Our algorithm is based on (a) the Tchebyshev representation of the unit circle image of a polynomial, (b) recent results on sign-definite decomposition and (c) bounded phase results from Robust Stability. These are combined to capture the unit circle image set of a polynomial over an interval set of controllers. The algorithm can be used recursively to obtain inner approximations of stabilizing sets. Examples are included to illustrate the algorithm.