Stabilizability of Unstable Linear Plants Under Bounded Control

Abstract

Considered in this paper is the problem of stabilizing a linear unstable plant under bounded control. It is shown that a linear strictly unstable plant can never be globally stabilized under bounded control, and a linear unstable plant can never be globally stabilized under bounded linear feedback control. Hence, any stabilizing controller {be it linear or nonlinear) for a strictly unstable plant can only be locally stabilizing. Consequently, it is important to estimate the domain of attraction achievable with a locally stabilizing control under a prespecified control bound. Since, it is difficult to construct the domain of attraction, we use the domain within which the control is not saturated to approximate it. The relation between these two domains are characterized and computable expressions for the biggest stability ball and the biggest stability polytope that lie inside the domain of nonsaturating control are given.