We consider a di erential inclusion system of the form _ x 2 Ax, where A is a collection of upper triangular matrices. Conditions for exponential stability of all the possible solutions are given.

In this paper, we investigate the problem of stability time-varying stochastic perturbed singular systems by using Lyapunov techniques under assumption that initial conditions are consistent. Sufficient on uniform exponential and practical in mean square solutions obtained based upon techniques. Furthermore, study stabilization some classes systems. Finally, provide numerical examples to valida...

Abstract We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on Popov’s hyperstability theorem. The main results are new bounds convergence rates perturbations damped harmonic oscillator, including Hessian-damped case, when satisfy certain sectoriality or convexity hypotheses. also include a simplified proof theorem in its general form, wh...

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(R,X),Lq(R,X)). We show that the admissibility of the pair (Lp(R,X),Lq(R,X)) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p ≥ q. As applications we obtain characterizations for uniform exponential dichotomy o...

In this paper, we mainly show the following two statements. (1) A discrete-time Markovian jump linear system is uniformly exponentially stable if and only if it is robustly periodically stable, by using a Gel’fand-Berger-Wang formula proved here. (2) A random linear ODE driven by a semiflow with closing by periodic orbits property is uniformly exponentially stable if and only if it is robustly ...