OPTIMAL SIMULTANEOUS STABILIZATION OF LINEAR SINGLE-INPUT SYSTEMS VIALINEAR STATE-FEEDBACK CONTROL

Simultaneous stabilization of a collection of linear time-invariant sy stems is considered. The aim is to develop a practical method for the design of a single feedback controller such that all the systems invol ved are stabilized with good transient responses. Hurwitz's necessary and sufficient conditions are used as the required set of constraints for simultaneous stability. For transient behaviour, we introduce the usual quadratic objective function as performance index for each syste m. Their sum is the objective function for the collection of systems a nd the problem is to minimize it by choosing a feedback gain vector su bject to boundedness and the Hurwitz stability constraints. A computat ional technique is proposed for solving this problem. The results obta ined give good transient behaviour. For illustration, two numerical ex amples are solved.