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New delay-dependent stability for systems with interval time-varying delay

Cui Y., Zhang T.

Przegląd Elektrotechniczny

2012

R. 88, nr 3b

97-99

This paper is concerned with the stability of systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, the improved delay-dependent stability criteria are derived. Because neither any model transformation nor free weighting matrices are employed in the theoretical derivation, the developed stability criteria simplify and improve the existing stability conditions. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods.

Analizowano stabilność systemów z interwałowym zmiennym w czasie opóźnieniem. Wyprowadzono nowe kryteria stabilności bazując na funkcjonale Lapunowa.

Observer-based controller design of time-delay systems with an interval time-varying delay

Thuan M. V., Phat V. N., Trinh H.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 4

921-927

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed \alfa-convergence rate. The design of an observer based output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.