A common Lyapunov function for a differential inclusion with matrices having small commutators. (30th December 2019)

• Record Type: Journal Article
• Authors: Gil', Michael
• Is Part Of: IFAC journal of systems and control. Volume 10(2019)
• Publication Date: 2019-12-30
• Subjects: Continuous-time switched systems -- Differential inclusion -- Common Lyapunov function -- Stability; Automatic control -- Periodicals; Relay control systems -- Periodicals; Embedded computer systems -- Periodicals; Feedback control systems -- Periodicals; Artificial intelligence -- Periodicals; Artificial intelligence; Automatic control; Embedded computer systems; Feedback control systems; Relay control systems; Electronic journals; Periodicals; 629.89
• DOI: 10.1016/j.ifacsc.2019.100072
• Languages: English
• ISSNs: 2468-6018

Abstract

Abstract: Let A 1 and A 2 be asymptotically stable matrices. We consider switched continuous time linear systems described by the differential inclusion x ̇ ( t ) = { y ( t ) : y ( t ) = A x ( t ), A ∈ { A 1, A 2 } } . The paper demonstrates that a common quadratic Lyapunov function exists for such systems, provided the commutator [ A 1, A 2 ] = A 1 A 2 − A 2 A 1 has a sufficiently small norm. Our results generalize the ones of Narendra and Balakrishnan (1994).