On stability of linear time-varying infinite-dimensional discrete-time systems. (English) Zbl 0543.93057

Author’s abstract: ”The asymptotic behaviour of linear time-varying infinite-dimensional discrete-time systems is considered. The introduced notions are: weak power equistability, power equistability, uniform power equistability, l\({}^ p\)-equistability, uniform \(l^ p\)-equistability and \(l^{p(x)}\)-equistability. It is shown that they are identical. A generalization of the concept of spectral radius of a single operator is also proposed. It is proven that any time-varying system is uniformly power equistable if and only if the generalized spectral radius of the sequence of the operators which define the system considered is less than one.”
Reviewer: R.Curtain


93D20 Asymptotic stability in control theory
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
93C99 Model systems in control theory
93C25 Control/observation systems in abstract spaces
Full Text: DOI


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