Global Optimization in Control Systems Analysis

Many problems in control system analysis and design can be posed in a setting where a linear system is affected by unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems can be performed only through an exhaustive search in parameter space (which is a rectangle in our case). We present a branch and bound algorithm that implements this search for the global optimum in a systematic manner; we then apply it to computing the minimum stability degree of a parameter-dependent linear system.