Optimal simultaneous stabilization of multi-model systems by state feedback controller (Q2704898)

Given a set of dynamical system \(\dot x_i= A_i x_i+ B_i u_i\), \(i= 1,2,\dots, m\) \((1< m<+\infty)\) the authors design a state feedback controller which simultaneously stabilizes and optimizes a given quadratic index. The asymptotic stability of the closed-loop system is ensured by a sufficient condition while the optimization is performed via a convex problem constrained by linear matrix inequalities which leads to the global optimum. Finally, two examples illustrate the obtained results.