Effective Computation of All Stabilizing Gain and Delay Regions for MIMO Systems

Abstract

This paper deals with determining all the loop gain and delay regions for closed-loop stability of a multivariable system. Such a problem admits no analytical solutions in general. Instead, we graphically determine stability boundaries in the gain-delay space based on the condition of the intersection of the characteristic loci with the critical point and decide stability of the regions divided by these boundaries with helps of a new perturbation analysis of parameters on change of closed-loop poles. This procedure yields all the stable regions, each of which captures the full information on the stabilizing loop gain interval versus any loop delay. The regions then also contain, as by- product, the information on gain and delay margins for stability. The stabilizing set is useful for stability robustness analysis, robust control design and system optimization. Several examples are provided to illustrate the effectiveness of the method.