The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak con...

The delay-dependent stability of singularly perturbed multiple time-delay systems with saturating actuators in slow states is discussed. A delay-dependent sufficient condition for the uniform asymptotic stability of the closed-loop systems via a memoryless state feedback controller are developed. The matrix measure and comparison theorem are employed to investigate the problem. The results obta...

We consider a switching system with time delay composed of a finite number of linear delay differential equations (DDEs). Each DDE consists of a sum of a linear ODE part and a linear DDE part. We study two particular cases: (a) all the ODE parts are stable and (b) all the ODE parts are unstable and determine conditions for delay independent stability. For case (a), we extend a standard result o...

This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler–Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrumdetermined growth condition,...

The global properties of a predator-prey model with stage structure for predator are studied using Lyapunov functionals and LaSalle’s invariance principle. It is found that, under hypotheses which insure the uniform persistence of the system and the existence of a unique positive steady state, a feasible a-priori lower bound condition on the abundance of the prey population ensures the global a...

We analyze the well-posedness and stability properties of a parameter dependent problem that models the reflection and transmission of electromagnetic waves at a thin and rapidly oscillating interface. The latter is modeled using approximate interface conditions that can be derived using asymptotic expansion of the exact solution with respect to the small parameter (proportional to the periodic...

We consider single class queueing networks with state-dependent arrival and service rates. Under the uniform (in state) stability condition, it is shown that the queue length process is V -uniformly ergodic; that is, it has a transition probability kernel which converges to its limit geometrically quickly in V -norm sense. Among several asymptotic properties of V -uniformly ergodic processes, w...

The article systematises and perform approaches the new concept of the ship autopilot in which control rules are derived for nonlinear controllers designed with the aid of the backstepping method and used for controlling the ship’s motion on its course. The objectives, approaches and problems were described. The design is very interesting has goals to create closed-loop systems with desirable s...

A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Numerical simulation...