Stabilization of discrete-time switched linear systems: Lyapunov-Metzler inequalities versus S-procedure characterizations*. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Kundu, A.; Daafouz, J.; Heemels, W.P.M.H.
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 3412
• Page End: 3417
• Publication Date: 2017-07
• Subjects: Discrete-time switched linear systems -- stabilizability -- min-switching strategy -- Lyapunov-Metzler inequalities -- S-procedure characterizations -- matrix inequalities; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.594
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: 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.