A common Lyapunov function for a differential inclusion with matrices having small commutators

Michael Gil’

doi:10.1016/j.ifacsc.2019.100072

A common Lyapunov function for a differential inclusion with matrices having small commutators

Michael Gil’

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let A₁ and A₂ be asymptotically stable matrices. We consider switched continuous time linear systems described by the differential inclusion ẋ(t)={y(t):y(t)=Ax(t),A∈{A₁,A₂}}. The paper demonstrates that a common quadratic Lyapunov function exists for such systems, provided the commutator [A₁,A₂]=A₁A₂−A₂A₁ has a sufficiently small norm. Our results generalize the ones of Narendra and Balakrishnan (1994).

Original language	English
Journal	IFAC Journal of Systems and Control
Volume	10
DOIs	https://doi.org/10.1016/j.ifacsc.2019.100072
State	Published - 30 Dec 2019

Keywords

Common Lyapunov function
Continuous-time switched systems
Differential inclusion
Stability

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Computer Science Applications
Computer Networks and Communications
Management Science and Operations Research
Artificial Intelligence

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10.1016/j.ifacsc.2019.100072

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abstract = "Let A1 and A2 be asymptotically stable matrices. We consider switched continuous time linear systems described by the differential inclusion ẋ(t)=\{y(t):y(t)=Ax(t),A∈\{A1,A2\}\}. The paper demonstrates that a common quadratic Lyapunov function exists for such systems, provided the commutator [A1,A2]=A1A2−A2A1 has a sufficiently small norm. Our results generalize the ones of Narendra and Balakrishnan (1994).",

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N2 - Let A1 and A2 be asymptotically stable matrices. We consider switched continuous time linear systems described by the differential inclusion ẋ(t)={y(t):y(t)=Ax(t),A∈{A1,A2}}. The paper demonstrates that a common quadratic Lyapunov function exists for such systems, provided the commutator [A1,A2]=A1A2−A2A1 has a sufficiently small norm. Our results generalize the ones of Narendra and Balakrishnan (1994).

AB - Let A1 and A2 be asymptotically stable matrices. We consider switched continuous time linear systems described by the differential inclusion ẋ(t)={y(t):y(t)=Ax(t),A∈{A1,A2}}. The paper demonstrates that a common quadratic Lyapunov function exists for such systems, provided the commutator [A1,A2]=A1A2−A2A1 has a sufficiently small norm. Our results generalize the ones of Narendra and Balakrishnan (1994).

KW - Common Lyapunov function

KW - Continuous-time switched systems

KW - Differential inclusion

KW - Stability

UR - https://www.scopus.com/pages/publications/85118330444

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DO - 10.1016/j.ifacsc.2019.100072

M3 - Article

AN - SCOPUS:85118330444

SN - 2468-6018

VL - 10

JO - IFAC Journal of Systems and Control

JF - IFAC Journal of Systems and Control

ER -

A common Lyapunov function for a differential inclusion with matrices having small commutators

Abstract

Keywords

ASJC Scopus subject areas

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