Systems & Control Letters
Nonquadratic Lyapunov functions for robust control
Automatica (Journal of IFAC)
Stability of Planar Switched Systems: The Linear Single Input Case
SIAM Journal on Control and Optimization
Stability and Stabilization of Continuous-Time Switched Linear Systems
SIAM Journal on Control and Optimization
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Hi-index | 22.14 |
In this paper, the stabilizability of discrete-time linear switched systems is considered. Several sufficient conditions for stabilizability are proposed in the literature, but no necessary and sufficient. The main contributions are the necessary and sufficient conditions for stabilizability based on the set-theory and the characterization of a universal class of Lyapunov functions. An algorithm for computing the Lyapunov functions and a procedure to design the stabilizing switching control law are provided, based on such conditions. Moreover, a sufficient condition for non-stabilizability for switched system is presented. Several academic examples are given to illustrate the efficiency of the proposed results. In particular, a Lyapunov function is obtained for a system for which the Lyapunov-Metzler condition for stabilizability does not hold.