earticle

영어

In this paper, we consider the design of stable linear switched systems for polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive an LMI to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.