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Uniform Exponential Stability for Time Varying Linear Dynamic Systems over Time Scales |
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PP: 115-118 |
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doi:10.18576/jant/050205
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Author(s) |
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Syed Omar Shah,
Akbar Zada,
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Abstract |
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| This paper proves the uniform exponential stability of the time varying linear dynamic system x ∆
(r) = G(r)x(r), r ∈ T in
terms of bounded-ness of solution of the following Cauchy problem: (W ∆ (r) = G(r)W(r)+
ω (r), 0 ≤ r ∈ T,
W(0) = v0,
where T denotes time scale, G(r) is a matrix valued function,
ω (r) is a bounded function on T and v0 ∈ Cm. In this note we prove the
results that have the above result as an immediate corollaries. |
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