Stochastic stability analysis of Markovian jump linear systems with incomplete transition descriptions

Composite anti‐disturbance control for semi‐Markovian jump systems with time‐varying delay and generally uncertain transition rates via disturbance observer

“…Markovian jump systems (MJSs) are special types of stochastic jump systems, which have been applied in many fields such as manufacturing, aerospace and network control. Many scholars have done numerous empirical research for the system with Markov process and reaped rich achievements [1, 2]. The stability and stabilisability of MJSs have been analysed in [3, 4].…”

Quantised control of delayed Markovian jump systems with partly known transition probabilities

“…Since then, the research of the Markovian jump systems with partly known transition probabilities has received extensive attention and some research results have also been obtained [10–13]. Recently, two new stability criteria have been derived in [14] for the continuous‐time and discrete‐time Markovian jump linear systems with partly known transition rates. The filtering method has been proposed in [15] for T‐S fuzzy singular Markov jump systems with general transition rates under the dynamic event‐based scheme, where sufficient conditions have been obtained to ensure stochastic admissibility and finite‐time boundness of the filtering error systems with the guaranteed mixed and passive performance.…”

“…In fact, if we do not consider the quantised control, then the system model in this work can be simplified to what is studied in [3] and the transition rates of the Markov chain are fully known in [3]. Moreover, different from [12,14,26], the system studied herein also considers more influencing factors, such as non-linearity, distributed delays and noise perturbation. It makes our system model more general.…”

“…It makes our system model more general. What's more, [12,14] analyse the asymp-totic stability and do not investigate the robustly exponential stability in the mean square and the quantised control problem. Compared with the uniform quantization with finite quantization interval, the logarithmic quantization provides a mapping within the whole interval.…”

“…Then, the major contributions and advantages of this paper can be generalised as follows: (1) the state feedback quantised control problem is addressed for a more general class of continuous-time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities; and (2) according to the known and unknown cases of the diagonal elements of the transition rate matrix, the corresponding stability criterion is given by introducing several new matrix inequality conditions. Moreover, a numerical example and a practical example (the dynamic model of the wheeled mobile manipulator in [14,45]) are presented to verify the feasibility and availability of the designed state feedback controller.…”