Stochastic Markovian Switching Systems Research Articles

Finite‐time annular domain stability and stabilization for stochastic Markovian switching systems driven by Wiener and Poisson noises

AbstractThis paper studies finite‐time annular domain stability (FTADS) and stabilization for stochastic Markovian switching systems driven by both Wiener and Poisson noises. Firstly, new sufficient conditions, based on the common parameter approach (CPA)/mode‐dependent parameter approach (MDPA), are presented to make the stochastic Markovian switching systems FTADS. Secondly, the finite‐time annular domain stabilization (FTAD‐stabilization) is discussed. The state feedback controller (SFC) and the dynamic output feedback controller (DOFC) are designed by CPA/MDPA, respectively, and some new sufficient conditions are given for the existence of these controllers. Moreover, an algorithm is presented to find the value ranges of some parameters, which shows the superiority of MDPA. Finally, a numerical example is supplied to verify the validity of our results.

Stabilization of stochastic Markovian switching systems on networks with multilinks based on aperiodically intermittent control: A new differential inequality technique

SummaryIn this paper, the stabilization problem of stochastic Markovian switching systems on networks with multilinks and time‐varying delays (SMNMT) is investigated via aperiodically intermittent control. At first, a new differential inequality is established for SMNMT, which relaxes the conditions of time‐varying delays compared with existing literature. Different from previous approaches of studying multilinks systems, new differential inequality technique combined with graph theory and Lyapunov method is adopted, based on which two types of sufficient conditions are derived to ensure the stability of SMNMT. The topological structure of multilinks systems on networks, stochastic perturbation, the transition rate of Markov chain, and intermittent control has a great impact on these developed conditions. The theoretical results are applied to stochastic Markovian switching oscillators networks with multilinks (SMONM), and a stabilization criterion of SMONM is derived as well. Finally, a numerical example is shown to illustrate the feasibility of our theoretical results.

Controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation

ABSTRACTThe paper deals with controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation by implying a new criterion for the domain of attraction firstly. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying stochastic stability of the plant are established. Then, the state feedback controller is designed to expand the domain of attraction of the corresponding closed-loop system. The procedure of deriving controller gain matrices is converted into an optimisation problem with constraints of a set of linear matrix inequalities. The mathematical model of RLC series circuit illustrates the validity of the obtained results.

Anti-windup design for stochastic Markovian switching systems with mode-dependent time-varying delays and saturation nonlinearity

This paper treats the problem of anti-windup design for stochastic Markovian switching systems with mode-dependent time-varying delays and saturation nonlinearity. The anti-windup compensator is designed such that the resulting system with mode-dependent time-varying delays and saturating actuator is stochastically stable and the domain of attraction is maximized. Sufficient conditions for the corresponding problem are proposed in terms of linear matrix inequalities. Finally, an example about RLC serial circuit demonstrates the validity of the proposed results.

Robust H-infinity Control for Stochastic Markovian Switching Systems Under Partly Known Transition Probabilities and Actuator Saturation via Anti-Windup Design

This paper deals with the problem of robust H-infinity control for stochastic Markovian switching systems with partly known transition probabilities and actuator saturation via anti-windup design. Under the assumption that output feedback controllers have been built to stabilize the stochastic Markovian switching system, anti-windup compensators are designed to expand the domain of attraction of the corresponding closed-loop system that contains admissible external disturbance, $$\hbox {It}\hat{o}$$Ito^-type stochastic disturbance, and norm-bounded parameter uncertainties. The procedure of deriving anti-windup compensation gain matrices is converted into an optimization problem with constraints of a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the validity of the main results.

Noise-Induced Stabilization of the Recurrent Neural Networks With Mixed Time-Varying Delays and Markovian-Switching Parameters

The stabilization of recurrent neural networks with mixed time-varying delays and Markovian-switching parameters by noise is discussed. First, a new result is given for the existence of unique states of recurrent neural networks (NNs) with mixed time-varying delays and Markovian-switching parameters in the presence of noise, without the need to satisfy the linear growth conditions required by general stochastic Markovian-switching systems. Next, a delay-dependent condition for stabilization of concerned recurrent NNs is derived by applying the ltd formula, the Gronwall inequality, the law of large numbers, and the ergodic property of Markovian chain. The results show that there always exists an appropriate white noise such that any recurrent NNs with mixed time-varying delays and Markovian-switching parameters can be exponentially stabilized by noise if the delays are sufficiently small.