One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters

The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained.

Spectral Perspective on the Stability of Discrete-Time Markov Jump Systems with Multiplicative Noise

We apply the spectrum analysis approach to address the stability of discrete-time Markov jump systems with state-multiplicative noise. In terms of the spectral distribution of a generalized Lyapunov operator, spectral criteria are presented to testify three different kinds of stochastic stabilities: asymptotic mean square stability, critical stability, and essential instability.

Lyapunov Theorems for the Asymptotic Behavior of Evolution Families on the Half-Line

Two theorems regarding the asymptotic behavior of evolution families are established in terms of the solutions of a certain Lyapunov operator equation.