Improved state estimation for Markovian jumping systems with time delay and partial information on transition probabilities

This paper focuses on the full‐order state estimation problem for continuous‐time Markovian jumping systems with time delay and incomplete transition probabilities. Based on the Lyapunov stability theory, an extended Wirtinger's inequality is used to value the upper bound of integral term by considering the relationship among time delay, its upper, and their difference. At the same time, an extended vector inequality is applied to deal with the accompanying fractions that contain the information of time delay. As a result, an improved stability criterion is derived, and a full‐order state estimates design method is proposed. Finally, two examples are provided to illustrate the merits of the proposed method.