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Stability of time-delay systems

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2 Author(s)
Lee, T.N. ; George Washington University, Washington, DC, USA ; Dianat, S.

This paper gives necessary and sufficient conditions for the stability of time-delay systems of the form \dot{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 solution P_{1}(0) of the algebraic nonlinear matrix equation A_{2} =e^{[A_{1}+P_{1}(0)]h}P_{1}(0) can be determined.

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Automatic Control, IEEE Transactions on  (Volume:26 ,  Issue: 4 )