Exponential stability of switched linear systems with time-varying delay.
Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays
The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.
Extrapolation methods to solve non-autonomous retarded partial differential equations
Using extrapolation spaces introduced by Da Prato-Grisvard and Nagel we prove a non-autonomous perturbation theorem for Hille-Yosida operators. The abstract result is applied to non-autonomous retarded partial differential equations.
Extremal Solutions for a Class of Functional Differential Equations
We study, in Carathéodory assumptions, existence, continuation and continuous dependence of extremal solutions for an abstract and rather general class of hereditary differential equations. By some examples we prove that, unlike the nonfunctional case, solved Cauchy problems for hereditary differential equations may not have local extremal solutions.
Extremal solutions of periodic boundary value problems for first-order impulsive integrodifferential equations of mixed-type on time scales.
Fault tolerant control for uncertain time-delay systems based on sliding mode control
Fault tolerant control for uncertain systems with time varying state-delay is studied in this paper. Based on sliding mode controller design, a fault tolerant control method is proposed. By means of the feasibility of some linear matrix inequalities (LMIs), delay dependent sufficient condition is derived for the existence of a linear sliding surface which guarantees quadratic stability of the reduced-order equivalent system restricted to the sliding surface. A reaching motion controller, which can...
Feedback control of time-delay systems with bounded control and state.
Feedback regulation of logistic growth.
Feeding Threshold for Predators Stabilizes Predator-Prey Systems
Since Rosenzweig showed the destabilisation of exploited ecosystems, the so called Paradox of enrichment, several mechanisms have been proposed to resolve this paradox. In this paper we will show that a feeding threshold in the functional response for predators feeding on a prey population stabilizes the system and that there exists a minimum threshold value above which the predator-prey system is unconditionally stable with respect to enrichment. Two models are analysed, the first being the classical...
Finite time stability and relative controllability of second order linear differential systems with pure delay
We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.
First order integro-differential equations in Banach algebras involving Carathéodory and discontinuous nonlinearities.
First-order differential equations with several deviating arguments: Sturmian comparison method in oscillation theroy: I.
Fixed point techniques and stability in nonlinear neutral differential equations with variable delays
Fixed point theorem in uniform spaces and applications
Fixed points and controllability in delay systems.
Fixed points and differential equations with asymptotically constant or periodic solutions.
Fixed points and stability in nonlinear equations with variable delays.
Fixed points, stability, and harmless perturbations.
Floquet boundary value problem of fractional functional differential equations.
Forbidden periods in delay differential equations.