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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