Stabilizability Analysis of Multiple Model Control with Probabilistic Switching

Abstract

In this paper, we derive some useful necessary conditions for stabilizability of multiple model control using a bank of stabilizing state feedback controllers. The outputs of this set are weighted by their probabilities as a soft switching system and together fed back to the plant. We study quadratic stabilizability of this closed loop soft switching system for both continuous and discrete-time hybrid system. For the continuous-time hybrid system, a bound on sum of eigenvalues of P_i is found when their derivatives of Lyapunov functions are upper bounded. For discrete-time hybrid system, a new stabilizability condition of soft switching signals is presented.