Stabilization of uncertain systems via linear control

This note considers the problem of stabilizing a linear dynamical system (Σ) whose state equation includes a time-varying uncertain parameter vector . Given the dynamics and a bounding set for the values , the objective is to choose a control law guaranteeing uniform asymptotic stability for all admissible variations of . Our results differ from previous work in one fundamental way; that is, we show that when working with linear controllers, it is possible to dispense with all assumptions on which have been made by previous authors (e.g., see [1]-[9]). This elimination of hypotheses on is accomplished roughly as follows: the system is shown to be equivalent to another system as far as stabilization is concerned. Since is a constant matrix (independent of ), the desired result is readily obtained.