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Robust finite‐time stability and stabilization problems for a class of linear uncertain time‐delay systems are studied. The concept of finite‐time stability is extended to linear uncertain time‐delay systems. Based on the Lyapunov method and properties of matrix inequalities, a sufficient condition that ensures finite‐time stability of linear uncertain time‐delay systems is given. By virtue of the results on finite‐time stability, a memoryless state feedback controller that guarantees that the closed‐loop system is finite time stable, is proposed. The controller design problem is solved by using the linear matrix inequalities and the cone complementarity linearization iterative algorithm. Numerical examples verify the efficiency of the proposed methods.

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Finite-time stability can be used in all applications where large values of the state are not acceptable. In this paper, finite-time stability problem for a class of linear time-varying delay systems is studied. Based on Lyapunov-like functions method and using an appropriate model transformation of the original system, the sufficient delay-dependent finite-time stability conditions are derived. The criteria are presented in the form of LMIs, which are dependent on the minimum and maximum delay bounds. The numerical examples are presented to illustrate the applicability of the developed results

For the first time, in this paper, a stability test procedure is proposed for linear time‐invariant fractional order systems (LTI FOS). Paper extends some basic results from the area of finite time and practical stability to linear, continuous, fractional order time invariant time‐delay systems given in state space form. Sufficient conditions of this kind of stability, for particular class of fractional time‐delay systems is derived.

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Abstract:This article deals with the problem of obtaining delay-dependent stability conditions for a class of discrete-time systems with interval time-varying delay. Using the decomposition the delay interval into two unequal subintervals by tuning parameter α, a new interval delay-dependent Lyapunov-Krasovskii functional is constructed to derive novel delay-dependent stability conditions which are expressed in terms of linear matrix inequalities. This leads to reduction of conservatism in terms of the upper bounds of the maximum time-delay. The numerical examples show that the obtained result is less conservative than some existing ones in the literature.