Stability of time-delay systems

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Title: Stability of time-delay systems
Author: Lee, T.; Dianat, Sohail
Abstract: This paper gives necessary and sufficient conditions for the stability of time-delay systems of the formdot{x}(t)=A_{1}x(t)+A_{2}x(t-h). These new conditions are derived by Lyapunov's direct method through systematic construction of the corresponding "energy" function. This function is known to exist, if a solutionP_{1}(0)of the algebraic nonlinear matrix equationA_{2} =e^{[A_{1}+P_{1}(0)]h}P_{1}(0)can be determined (Refer to PDF file for exact formulas).
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Date: 1981-08

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