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The paper demonstrates that a common quadratic Lyapunov function exists for all linear systems of the form x/spl dot/=A/sub i/x, i=1,2,/spl middot//spl middot//spl middot/,N, where the matrices A/sub i/ are asymptotically stable and commute pairwise. This in turn assures the exponential stability of a switching system x/spl dot/(t)=A(t)x(t) where A(t) switches between the above constant matrices A/sub i/.>
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Narendra et al. (1994) studied this question.
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