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We provide necessary and sufficient conditions in terms of the existence of common Lyapunov functions for switched systems with modes governed by strongly continuous semigroups on Banach spaces to be globally uniformly exponentially stable for arbitrary switching signals.
The well-possedness and exponential stability of the solution to a multi-state system with two repair distributions were discussed by applying the C0 semigroups theory of function analysis. First, the integro-differential equations described the system was transformed into some abstract Cauchy problem on some suitable Banach space. Second, by Hill-Yosida Theorem, the system operator generates a positive...
The robustness with respect to small delays for exponential stability of a class of infinite-dimensional linear dynamical system with unbounded delay operator is studied in Banach space. In terms of the theory of fundamental operator family and the theory of operator-valued Fourier multipliers, a frequency-domain characterization for the robust exponential stability with respect to small delays is...
In this paper, the solution of a warm standby repairable human-machine system with two identical units is investigated. By using the method of functional analysis, especially, the linear operator theory on Banach space, we prove the existence of the strictly dominant eigenvalue, and we show the linear stability and the exponential stability of solution.
In this paper, the solution of a transfer line with a reliable machine, an unreliable machine and storage buffer is investigated. By using the method of functional analysis, especially, the linear operator theory on Banach space, we prove the existence of the strictly dominant eigenvalue, and show the linear stability and the exponential stability of solution.
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