Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Time Delay Autonomous Systems
نویسنده
چکیده
This paper offers new, necessary and sufficient conditions for delay-dependent asymptotic stability of systems of the form 0 1 ( 1) ( ) ( ) x k A x k A x k h + = + − . The time-dependent criteria are derived by Lyapunov’s direct method. Two matrix equations have been derived: matrix polynomial equation and discrete Lyapunov matrix equation. Also, modifications of the existing sufficient conditions of convergence of Traub and Bernoulli algorithms for computing the dominant solvent of the matrix polynomial equation are derived. Numerical computations are performed to illustrate the results obtained.
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