Lie-Algebraic Criterion for Stability of Switched Differential-Algebraic Equations. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Raj, Phani; Pal, Debasattam
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 2004
• Page End: 2009
• Publication Date: 2020
• Subjects: Switched differential-algebraic equations -- hybrid systems -- exponential stability; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.2702
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper, we prove a Lie algebraic result for stability of switched DAEs with a common descriptor matrix (common E matrix). We first show that if a switched DAE with a common descriptor matrix is asymptotically stable, then it is also globally uniformly exponentially stable. We then show that switched DAEs with common descriptor matrix and consistent block upper triangular structure is globally uniformly exponentially stable if and only if the switched DAEs corresponding to the diagonal blocks are globally uniformly exponentially stable. Finally, we show that a switched DAE with common descriptor matrix, stable and impulse free DAE subsystems, is globally uniformly exponentially stable (GUES) if there exists an invertible matrix N such that the Lie algebra {N E, N Ai : i ϵ P}LA is solvable.