This paper addresses the stability analysis problem for a class of linear hyperbolic systems with distributed controllers sampled in space and time. First, considered system is recast an equivalent form continuous time control loop operators representing discretization errors (spatio-temporal sampling errors). Then help Lyapunov–Razumikhin approach, Rɛ-stability proposed balance laws verified v...

and Applied Analysis 3 Definition 2.1. The trivial solution of system 2.2 is said to be globally exponentially stable, if there exist numbers λ > 0 and M 1 such that ∣∣x(t, t0, φ )∣∣ M∥∥φ∥∥e−λt, t 0, 2.3 whenever φ ∈ PC. Definition 2.2. V : −τ,∞ ×Rn → R is said to belong to the class ν0, ifV is continuous on each of the sets tk−1, tk × R, lim t,y → t− k ,x V t, y V tk, x exists, V t, x is local...

This paper focuses on the problem of pth moment and almost sure exponential stability impulsive neutral stochastic functional differential equations (INSFDEs). Based Lyapunov function average dwell time (ADT), two sufficient criteria for INSFDEs are derived, which manifest that result obtained in this is more convenient to be used than those Razumikhin conditions former literature. Finally, num...

This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may b...

The nonlinear time-delay systems are considered and the limiting Behavior of their solutions is investigated. case in which have a trivial equilibrium that may not be an invariant set system studied. junction Lyapunov - Krasovskii Razumikhin approaches applied to obtain sufficient conditions for existence asymptotic quiescent position large. In when general has solution, new its stability obtai...

Abstract In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, define in an appropriate way initial conditions which are deeply connected the derivative used. We introduce generalization practical stability call time. Several sufficient for time obtained using Lyapunov functions and modified Razumikhin technique. Two types derivati...