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An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales

Abstract and Applied Analysis
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We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, 𝜓 -uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

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