22 research outputs found
Analyzing stability of a delay differential equation involving two delays
Analysis of the systems involving delay is a popular topic among applied
scientists. In the present work, we analyze the generalized equation
involving two delays
viz. and . We use the the stability conditions to
propose the critical values of delays. Using examples, we show that the chaotic
oscillations are observed in the unstable region only. We also propose a
numerical scheme to solve such equations.Comment: 10 pages, 7 figure
Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality
This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems
Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach
In this paper, a stability test procedure is proposed for linear nonhomogeneous fractional order systems with a pure time delay. Some basic results from the area of finite time and practical stability are extended to linear, continuous, fractional order time-delay systems given in state-space form. Sufficient conditions of this kind of stability are derived for particular class of fractional time-delay systems. A numerical example is given to illustrate the validity of the proposed procedure
Finite-time stability analysis of fractional order time delay systems: Bellman-Gronwall's approach
Ovaj rad proširuje neke osnovne rezultate iz oblasti praktične stabilnosti i stabilnosti na konačnom vremenskom intervalu na nelinearne, perturbovane sisteme sa kašnjenjem necelobrojnog reda gde je predložen postupak testiranja robusne stabilnosti. Proučavan je problem dovoljnih uslova koji omogućavaju da trajektorije sistema ostaju unutar a priori zadatih skupova i to za posebnu klasu nelinearnih sistema sa kašnjenjem necelobrojnog reda.The paper extends some basic results from the area of finite time and practical stability to nonlinear, perturbed, fractional order time-delay systems where a robust stability test procedure is proposed. The problem of sufficient conditions that enable system trajectories to stay within the a priori given sets for the particular class of nonlinear fractional order time delay systems is examined
Finite-time stability analysis of fractional order time delay systems: Bellman-Gronwall's approach
Ovaj rad proširuje neke osnovne rezultate iz oblasti praktične stabilnosti i stabilnosti na konačnom vremenskom intervalu na nelinearne, perturbovane sisteme sa kašnjenjem necelobrojnog reda gde je predložen postupak testiranja robusne stabilnosti. Proučavan je problem dovoljnih uslova koji omogućavaju da trajektorije sistema ostaju unutar a priori zadatih skupova i to za posebnu klasu nelinearnih sistema sa kašnjenjem necelobrojnog reda.The paper extends some basic results from the area of finite time and practical stability to nonlinear, perturbed, fractional order time-delay systems where a robust stability test procedure is proposed. The problem of sufficient conditions that enable system trajectories to stay within the a priori given sets for the particular class of nonlinear fractional order time delay systems is examined
On the mixed sensitivity minimization for systems with infinitely many unstable modes
In this note we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers and a data transformation, we show that ℋ ∞ controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes. © 2004 Elsevier B.V. All rights reserved
Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays
This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gronwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result