No abstract

This paper pays close attention to the reachable set synthesis problem for discrete‐time delayed Markovian jump systems (DDMJSs) under partially asynchronous control. Different from the traditional controller, a class of partially asynchronous controller is proposed, where delay‐free and delay states are comprised and cannot take place at the same time. In addition, Bernoulli variable is used to describe the probability distribution of the above two kinds of states, and the design of feedback controller is considered. On this basis, the sufficient conditions which the state feedback controller is existent are solved effectively by using linear matrix inequalities (LMIs). Furthermore, the results of reachable set synthesis are extended to the DDMJs with uncertain transition probabilities. Finally, several numerical simulations are given to show the effectiveness of the presented methods.

This paper considers the observer design problem of continuous-time delayed Markovian jump systems with output state saturation. Different from the traditionally observer-based saturation control methods, a kind of system output state saturation with a partially delay-dependent property is proposed, where both nondelay and delay states exist at the same time but happen asynchronously. By exploiting the Bernoulli variable, the probability distributions of such two states are described and considered in the observer design. Based on an improved equality applied to deal with saturation terms, sufficient conditions for the designed observer with three kinds of output saturations are all provided with LMI forms. Finally, a numerical example is given to indicate the effectiveness of the obtained results.

This note addresses the asynchronous state-feedback control (ASC) for delay nonlinear Markovian jump systems (DNMJSs) subject to reachable set boundary. Under taking time-varying delays and external disturbance into consideration, Takagi-Sugeno fuzzy model is adopted to approximate the nonlinear dynamics systems. Although the assumption about time-delay is practical, it will cause subsystem modes to be not synchronous with the controller modes. As a consequence, the description method of the nonsynchronous phenomenon is introduced, which is a hidden Markov model. Furthermore, an available ASC is designed and all reachable states of the system is constrained within the compact ellipsoidal boundary to guarantee the safe operation of the DNMJSs. The existence conditions of the desired ASC are obtained via solving a group of feasible linear matrix inequalities. Finally, some numerical simulations are provided to verify the availability of the proposed method in this article.

No abstract