We present an optimal model based on utility functions and pricing for downlink radio resource allocation in code division multiple access (CDMA) systems. The aim of this model is to achieve the throughput maximization via dynamic price adjustment. Due to the existence of action delays, we give globally asymptotical stability results using Lyapunov-Razumikhin arguments for rate and price evolve...

This paper is concerned with an almost periodic Volterra integro dynamic equation on time scales. Based on the theory of calculus on time scales, by using differential inequality theory and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the global attractivity of the system are obtained. Then, by using the properties of almost periodic func...

We study the safety problem for nonlinear nonautonomous systems described by Cauchy differential equation with delay ordinary derivative. To analyze safety, we introduce Razumikhin barrier function that guarantees invariance of some set. Unlike traditional functions used in optimization problems, our construction is not unbounded on boundary an admissible domain, but only changes sign. Owing to...

The purpose of this paper is to investigate some qualitative properties solutions nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo derivatives. These include uniform stability, asymptotic Mittag–Leffer stability and boundedness. presented results are proved by defining an appropriate Lyapunov function applying the Lyapunov–Razumikhin method (LRM). Henc...

Although deterministic interval systems have received a great deal of attention, so far there is no work on stochastic interval systems. The main aim of this paper is to initiate the study of stochastic interval systems. Of course there are many properties of such systems to be investigated, but this paper will concentrate on the study of exponential stability of stochastic interval systems wit...

In this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov-Razumikhin technique for neutral equations with finite del...

This paper is devoted to stability analysis of linear systems with state delay and input saturation. The domain of attraction resulting from an a priori designed state feedback law is analyzed using Lyapunov–Razumikhin and Lyapunov–Krasovskii functional approach. Both delay-independent and delay-dependent estimation of the domain of attraction are presented using the linear matrix inequality te...