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A special type of asymptotic (exponential) stability, namely componentwise asymptotic (exponential) stability for the continuous-time interval system is investigated. A set-valued map that represents the constraint of the state of the system is defined. And, by applying the viability theory of differential equation, sufficient and necessary conditions for the componentwise asymptotical (exponential) stability of this kind of systems are given.
A special type of asymptotic (exponential) stability for the component-wise asymptotic (exponential) stability for the continuous-time interval system is investigated. A set-valued map that represents the constraint of the state of the system is defined. And, by applying the viability theory of differential equation, sufficient and necessary conditions for the componentwise asymptotical (exponential) stability of this kind of systems are given.