Sign Stability of Dual Switching Linear Continuous-Time Positive Systems

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but not their structures of magnitude, are key information that causes a qualitative concept of stability called sign stability. Both 1-moment exponential stability and EMS stability, which are the traditional stability concepts, are generalized intrinsically. Hence, both 1-moment exponential sign stability and EMS sign stability are introduced and are proven based on sign equivalency. It is shown that they are symmetrically and qualitatively stable. Notably, the notion of stability can be checked quantitatively using some examples.

The exponential behavior and stabilizability of quasilinear parabolic stochastic partial differential equation

In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the solutions are established. Moreover, under certain hypothesis on the stochastic perturbations, pathwise exponential stability can be derived, without utilizing the mean square stability.

Exponential mean-square stability properties of stochastic linear multistep methods

The aim of this paper is the analysis of exponential mean-square stability properties of nonlinear stochastic linear multistep methods. In particular it is known that, under certain hypothesis on the drift and diffusion terms of the equation, exponential mean-square contractivity is visible: the qualitative feature of the exact problem is here analysed under the numerical perspective, to understand whether a stochastic linear multistep method can provide an analogous behaviour and which restrictions on the employed stepsize should be imposed in order to reproduce the contractive behaviour. Numerical experiments confirming the theoretical analysis are also given.

Stability of switched Markovian jump systems with time-varying generally bounded transition rates

This paper addresses the exponential mean-square stability for a kind of switched Markovian jump systems, which have time-varying generally bounded transition rates and mode-dependent time delay. Since these transition rates are time-varying and generally bounded, they turn out to be more practical. In fact, those existing transition rates can be treated as special cases of the proposed ones in this paper. By constructing a new Lyapunov-Krasovskii function, sufficient conditions in a tractable form are derived for the exponential mean-square stability of the considered systems. For good measure, a numerical example is given to show the efficiency and potential of the proposed method.

On the stability of solutions to stochastic 2D g-Navier–Stokes equations with finite delays

In this paper, we study the exponential mean square stability and almost sure exponential stability of weak solutions to the stochastic 2D