A positive real lemma for singular hybrid systems. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Park, Chan-eun; Park, In Seok; Kwon, Nam Kyu; Park, PooGyeon
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 2051
• Page End: 2056
• Publication Date: 2020
• Subjects: Stochastic hybrid systems -- stability -- stabilization of hybrid systems -- linear matrix inequality -- positive real lemma -- descriptor system; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.2518
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper introduces a positive real lemma for continuous-time singular hybrid systems. The necessary and sufficient condition of stochastic admissibility and strict passivity for the singular hybrid systems is obtained in terms of linear matrix inequalities. The sufficient condition is derived by using mode-dependent Lyapunov function. In this step, two slack variables are inserted to make the proposed condition be necessary and sufficient condition in terms of strict linear matrix inequalities. Then, to prove the necessary condition, the positive real lemma for the hybrid system is proposed. Since the admissible singular system can be reformulated into stable normal system, the positive real lemma for the hybrid system holds. Thus, we give a necessary condition by constructing the solution of the proposed lemma from that of the hybrid systems.