By Dragutin Debeljkovic
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Extra resources for Time-Delay Systems
Debeljkovic, D. , N. A. Kablar, (1999) Finite time stability of linear singular systems: Bellman - Gronwall approach, Proc. ACC 99, San Diego (USA), pp. 1803-1806. Debeljkovic, D. , S. A. Milinkovic, S. B. Stojanovic, (2004) Stability of Time Delay Systems over Finite and Infinite Time Interval, Cigoja press, Belgrade, ISBN 86-7558-212-9 Debeljkovic D. , Lj. A. , N. S. Visnjic, M. Pjescic, (2007) Asymptotic Stability of Generalized Discrete Descriptive Time Delayed Systems, Proc. The 5th Edition of IFAC Know.
Throughout this exposure it is assumed that ( λ E − A ) is invertible at all but a finite number ( ) of points λ ∈ C and hence that if a solution x ( k ) , ( k ≥ 0 ) of x ( k ) : k = 0,1,... exists for a given choice of x 0 , it is unique, (Campbell 1980). The linear discrete descriptor system is said to be stable if (37) is regular and all of its finite poles are within region Ω(0,1), (Dai 1989), so careful investigation shows there is no need for the matrix A to be invertible, in comparison with continuous case, see (Debeljkovic et al.
Debeljkovic, Lj. D. & D. H. Owens, (1985) On practical stability of singular systems, Proc. 85, October 85, Madrid (Spain), pp. 103-105. Debeljkovic, D. Lj. & D. H. Owens, (1986) On non - Lyapunov stability of discrete-descriptor systems, Proc. EUROCON Conference 86, 21 – 23 April, Paris (France), pp. 406-409. Debeljkovic, D. , V. B. Bajic, A. U. Grgic, S. A. Milinkovic, (1995) Non-Lyapunov stability and instability robustness consideration for linear singular systems, Proc. 3rd ECC, Roma (Italy), September 5 – 8, pp.
Time-Delay Systems by Dragutin Debeljkovic