Stabilization of discrete-time switched linear systems: Lyapunov-Metzler inequalities versus S-procedure characterizations

作     者：Kundu A. Daafouz J. Heemels W.P.M.H. 

作者机构：Robert Bosch Centre for Cyber-Physical Systems Indian Institute of Science Bangalore India Centre for Research in Automatic Control of Nancy University of Lorraine France Control Systems Technology Group Department of Mechanical Engineering Eindhoven University of Technology Netherlands 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2017年第50卷第1期

页      面：3412-3417页

主　　题：Discrete-time switched linear systems Lyapunov-Metzler inequalities matrix inequalities min-switching strategy S-procedure characterizations stabilizability 

摘      要：In this paper we study connections between Lyapunov-Metzler inequalities and S-procedure characterizations in the context of stabilizing discrete-time switched linear systems using min-switching strategies. We propose two generalized versions of S-procedure characterization along the lines of the generalized versions of Lyapunov-Metzler inequalities recently proposed in the literature. It is shown that the existence of a solution to the generalized version(s) of Lyapunov-Metzler inequalities is equivalent to the existence of a solution to the generalized version(s) of S-procedure characterization with a restricted choice of the scalar quantities involved in the latter. This recovers some of our earlier works on the classical Lyapunov-Metzler inequalities as a special case. We also highlight and discuss an open question of whether the generalized versions of S-procedure characterization are strictly less conservative than the generalized versions of Lyapunov-Metzler inequalities, which in turn are equivalent to periodic stabilizability as was recently shown. © 2017