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We consider a general class of distributed algorithms for the control of power allocations in time-dependent wireless networks. We employ appropriately constructed Lyapunov functions to show that any bounded power distribution obtained from these algorithms is uniformly asymptotically stable. Further, we use Lyapunov-Razumikhin functions to show that even when the system incorporates heterogeneous,...
This paper gives new contributions to the area of non-Lyapunov (finite time stability, technical stability, practical stability, final stability) for the particular class of linear discrete time delay systems. The idea of attractive practical stability is introduced for the first time. Moreover, based on the matrix inequalities and Lyapunov-like functions, some new sufficient conditions under which...
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 discrete time delay systems have been investigated...
The article provides sufficient conditions for both practical and finite time stability of linear continuous time delay systems described as X(t) = A0X(t) + A1X(t − τ). Considering a finite time stability concept, the new delay independent conditions have been derived using the approach based on the Lyapunov-like functions. These functions do not need to have the properties of positivity in the whole...
This paper gives sufficient conditions for the practical and finite time stability of linear continuous time delay systems of the form X(t)=A0X(t)+A1X(t−τ). When we consider finite time stability, these new, delay independent conditions are derived using the approach based on Lyapunov-Krassovski functionals. In this case these functionals need not to have: a) properties of positivity in whole state...
This paper gives sufficient conditions for the practical and finite time stability of linear continuous time delay systems of the form ẋ(t) = A0x(t) + A1x(t − τ). When we consider finite time stability, these new, delay independent conditions are derived using the approach based on Lyapunov-Krassovski functionals. In this case these functionals need not to have: a) properties of positivity in whole...
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 state space as well as negative derivatives...
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