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Our aim is to improve the existing results concerning asymptotic stability of a particular class of linear discrete time delay systems. This work extends one of the basic results in the area of Lyapunov (asymptotic) to linear, discrete, time invariant time-delay systems. This result is given in the form of only sufficient conditions and represent further(More)
This paper gives sufficient conditions for the practical and finite time stability of a particular class of linear discrete time delay systems. Analyzing the finite time stability concept, these new delay-independent conditions are derived using an approach based on the Lyapunov-like functions. The practical stability and attractive practical stability for(More)
Medical-technical robotic systems are typical examples in which external contact forces on a system play an important role in the system dynamics. Mathematical modeling of these systems is challenging due to a variety of reasons. Mathematical models for the described class of systems contain differential equations with an associate algebraic equation, which(More)
This paper extends some of the basic results in the area of Lyapunov (asymptotic) and finite time and practical stability to linear, discrete, time invariant time-delay systems. New definitions have been established for the latter concept of stability. Sufficient conditions for this type of stability, concerning the particular class of linear discrete(More)
This paper gives sufficient conditions for the stability of linear singular discrete delay systems of the form Ex/spl dot/(t) = A/sub 0/x(t) + A/sub 1/x(t - /spl tau/). These new, delay-independent conditions are derived using approach based on Lyapunov's direct method. A numerical example has been working out to show the applicability of results derived.(More)
This paper provides sufficient conditions for the asymptotic practical and finite time stability of linear continuous time delay systems mathematically described as x'(t)= A<sub>0</sub>x(t) - A<sub>1</sub>x(t - &#x03C4;). The Lyapunov-Krassovski functionals were used to establish the novel delay independent conditions. These conditions were applied in the(More)
In this article the sufficient conditions for the practical and finite-time stability of the linear continuous systems with the time-delay are presented. The new delay-independent stability conditions are derived using Lyapunov-like functions for the finite-time systems. For these functions it is not necessary to have properties of positivity in the whole(More)