Stabilization by delay distributed feedback control

Abstract

In this paper, a new approach to stability of integro-differential equations x (t) + β1 t t−τ 1 (t) e −α 1 (t−s) x (s) ds + β2 t t−τ 2 (t) e −α 2 (t−s) x (s) ds = 0 and x (t) + β1 t−τ 1 (t) 0 e −α 1 (t−s) x (s) ds + β2 t−τ 2 (t) 0 e −α 2 (t−s) x (s) ds = 0 is proposed. Under corresponding conditions on the coefficients α1, α2, β1 and β2 the first equation is exponentially stable if the delays τ1 (t) and τ2 (t) are large enough and the second equation is exponentially stable if these delays are small enough. On the basis of these results, assertions on stabilization by distributed input control are proven. It should be stressed that stabilization of this sort, according to common belief, requires a damping term in the second order differential equation. Results obtained in this paper demonstrate that this is not the case.

Around the Model of Infection Disease: The Cauchy Matrix and Its Properties

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Stability of functional differential systems applied to the model of testosterone regulation

“…It is pointed out in [23] that models with distributed inputs can appear in population dynamics, in propellant rocket motors, and in network control systems. Sufficient conditions of stability for IDE (1.1) were obtained in many well-known works (see, for example, [7,8,14,24,25,29]).…”

Distributed Control and the Lyapunov Characteristic Exponents in the Model of Infectious Diseases

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