STABILITY OF LINEAR TIME-INVARIANT OPEN-LOOP UNSTABLE SYSTEMS WITH INPUT SATURATION

This paper analyzes the stability of a linear time-invariant open-loop unstable system subject to input saturation. First, we extend the idea of approximating the locally asymptotically stable region (controllable set) of the system for the case where the control is small enough to be unsaturated (inside the linear region), to the case when the control is allowed to saturate. It is shown that, when the Lyapunov descent criterion and the Kuhn-Tucker Theorem is applied, a superior locally asymptotically stable region is found. A technique for approximating the locally asymptotically stable region is presented