Abstract. Many real processes can be modeled by stochastic differential equations with aftereffect [1]-[3]. Stability conditions for such systems can be obtained by construction of appropriate Lyapunov functionals using special procedure of Lyapunov functionals construction [4]-[14]. In this paper asymptotic mean square stability of stochastic linear differential equations with discrete and dis...

In this study, delay-dependent robust stability problem is investigated for uncertain neutral systems with discrete and distributed delays. By constructing an augmented Lyapunov-Krasovskii functional involving triple integral terms and taking into account the relationships between the different delays, new less conservative stability and robust stability criteria are established first using the...

In this paper we describe the maximal and the minimal values of Lyapunov exponents for second order discrete time invariant linear system perturbed by time varying bounded perturbation. The results may be interpreted in terms of generalized spectral radius and applied to obtained formulas for robust stability problem. Key-Words: Time varying discrete linear systems, Lyapunov exponents, robust s...

Differential equations with discontinuous righthand side and solutions intended in Carathéodory sense are considered. For these equations sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.

One of the most fundamental results in analysing the stability properties of periodic orbits and limit cycles of dynamical systems is Poincaré’s theorem. The proof of this result involves system analytic arguments along with the Hartman–Grobman theorem. Using the notions of stability of sets, lower semicontinuous Lyapunov functions are constructed to provide a Lyapunov function proof of Poincar...