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When Is σ ( A ( t )) ⊂ { z ∈ ℂ; ℜ z ≤ − α < 0} the Sufficient Condition for Uniform Asymptotic Stability of LTV System ẋ = A ( t ) x ?

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  • Robert Vrabel

    (Institute of Applied Informatics, Automation and Mechatronics, Slovak University of Technology in Bratislava, Bottova 25, 917 01 Trnava, Slovakia)

Abstract

In this paper, the class of matrix functions A ( t ) is determined for which the condition that the pointwise spectrum σ ( A ( t ) ) ⊂ z ∈ C ; ℜ z ≤ − α for all t ≥ t 0 and some α > 0 is sufficient for uniform asymptotic stability of the linear time-varying system x ˙ = A ( t ) x . We prove that this class contains as a proper subset the matrix functions with the values in the special orthogonal group S O ( n ) .

Suggested Citation

  • Robert Vrabel, 2022. "When Is σ ( A ( t )) ⊂ { z ∈ ℂ; ℜ z ≤ − α < 0} the Sufficient Condition for Uniform Asymptotic Stability of LTV System ẋ = A ( t ) x ?," Mathematics, MDPI, vol. 10(1), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:141-:d:717320
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