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 ?

Robert Vrabel
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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

Mathematics, 2022, vol. 10, issue 1, 1-12

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 ) .

Keywords: linear time-varying system; stability; logarithmic norm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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