Population dynamics driven by truncated stable processes with Markovian switching

Stability in distribution of neutral stochastic functional differential equations with Markovian switching

In this paper, we investigate the problem of pth-moment stability of stochastic functional differential equations with Markovian switching and impulsive control via comparison principle. Employing stochastic analysis theory and an impulsive delay differential inequality, we establish a new comparison principle for stochastic functional differential equations with Markovian switching and impulsive control. Using the comparison principle, we derive sufficient conditions for stochastic functional differential equations with Markovian switching and impulsive control by the stability of impulsive delay differential equations. An example is provided to show the effectiveness of the proposed results.

Almost sure H∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

Mean-square exponential input-to-state stability of delayed Cohen–Grossberg neural networks with Markovian switching based on vector Lyapunov functions

In this paper we discuss the $p$th moment absolute exponential stability of stochastic control system with Markovian switching. We first give a new concept of $p$th moment absolute exponential stability, then we establish some theorems under different hypotheses to guarantee the system $p$th moment absolutely exponentially stable. These sufficient conditions in our theorems are algebraic criteria in terms of matrix inequalities, and we introduce an $M$-method with MATLAB to compute them. Finally, some examples are given to illustrate our results.

Stationary distribution and ergodicity of a stochastic hybrid competition model with Lévy jumps

The aim of this work is to study the asymptotic stability of the time-changed stochastic delay differential equations (SDDEs) with Markovian switching. Some sufficient conditions for the asymptotic stability of solutions to the time-changed SDDEs are presented. In contrast to the asymptotic stability in existing articles, we present the new results on the stability of solutions to time-changed SDDEs, which is driven by time-changed Brownian motion. Finally, an example is given to demonstrate the effectiveness of the main results.

Neutral stochastic dynamic systems have received broad attention, because the problems are not only great theoretical significance, but also have played an important role in many ways such as engineering control, finance, communication equipment, social science, etc. In this paper, we consider stability of neutral stochastic partial differential dynamic systems with Markovian switching. Some new sufficient conditions proving the stability in mean square of this neutral stochastic dynamic systems are derived by employing the fixed point approach. Some well-known results are improved and generalized.

In this article, we discuss a class of stochastic partial differential systems with nonlinear impulsive and Markovian switching. Some new sufficient conditions proving asymptotic stability in p-th moment of stochastic systems are derived by employing some inequality and the fixed point technique. Some well-known results are generalized and improved.

In this letter, the analysis problem of adaptive exponential synchronization in pth moment is considered for neutral-type neural networks with time delays and Markovian switching. By utilizing a new nonnegative function and the M-matrix approach, several sufficient conditions to ensure the adaptive exponential synchronization in pth moment for neutral-type neural networks are derived. Via the adaptive feedback control techniques, some suitable parameters update laws are found. To illustrate the effectiveness of the M-matrix-based synchronization conditions derived in this letter, numerical example is provided finally.

A problem of state output feedback stabilization of discrete-time stochastic systems with multiplicative noise under Markovian switching is considered. Under some appropriate assumptions, the stability of this system under pure impulsive control is given. Further under hybrid impulsive control, the output feedback stabilization problem is investigated. The hybrid control action is formulated as a combination of the regular control along with an impulsive control action. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the stochastic and the deterministic terms. Sufficient conditions based on stochastic semi-definite programming and linear matrix inequalities (LMIs) for both stochastic stability and stabilization are obtained. Such a nonconvex problem is solved using the existing optimization algorithms and the nonconvex CVX package. The robustness of the stability and stabilization concepts against all admissible uncertainties are also investigated. The parameter uncertainties we consider here are norm bounded. Two examples are given to demonstrate the obtained results.

This paper considers the stabilisation of high-order nonlinear stochastic delayed coupled systems with Markovian switching (HNSMS) by periodically intermittent control (PIC). Notably, the coefficients in HNSMS no longer satisfy the linear growth condition. In the mean time, PIC is first introduced to ensure the stabilisation of HNSMS. Since current Halanay-type differential inequalities (H-type inequalities) are not applicable to high-order nonlinear systems with PIC, a generalised H-type inequality with high-order terms for such systems is established, in which the order of high-order terms can be different. Together with graph theory and Lyapunov method, some sufficient conditions reaching the stability are presented. Then, our results are used to study the stability of modified Van der Pol–Duffing oscillators with Markovian switching. Ultimately, the effectiveness of theoretical results is checked by a numerical test.

In this paper, we investigate the synchronization of stochastic complex networks with Markovian switching via aperiodically intermittent pinning control. The major spot of this work is that the complex network is subject to noise perturbations, Markovian switching internal and outer time-varying delays. Sufficient conditions for synchronization are derived though employing aperiodically intermittent pinning control technique, the Lyapunov functional method, Ito's formula and Gronwall inequality. Finally, numerical simulations are given to demonstrate the applicability and validity of the theoretical results.

In this paper, we consider ${\mathcal{H}_\infty }$admissibility of singular stochastic systems with Markovian switching (SSMS) with partly unknown transition rates (PUTR). Until now, ${\mathcal{H}_\infty }$admissibility condition for SSMS have been studied for the limited cases: 1) SSMS which do not have a path from disturbances to the desired output, 2) the sufficient condition for the general SSMS. On the other hand, the authors successfully obtain the equivalent condition of ${\mathcal{H}_\infty }$admissibility criterion for SSMSs by introducing two slack variables. Also, because the proposed condition is expressed in terms of convex condition, i.e., linear matrix inequalities (LMIs), the result can be used to find the optimal ${\mathcal{H}_\infty }$performance even though the information about the transition rates is limited.

We present Lyapunov-type conditions for non-strong ergodicity of Markov processes. Some concrete models are discussed, including diffusion processes on Riemannian manifolds and Ornstein–Uhlenbeck processes driven by symmetric $\alpha$-stable processes. In particular, we show that any process of d-dimensional Ornstein–Uhlenbeck type driven by $\alpha$-stable noise is not strongly ergodic for every $\alpha\in (0,2]$.