Resilient and finite‐time H∞$$ {H}_{\infty } $$ control of semi‐Markov jump systems with both upper and lower thresholds of sojourn time.

This article discusses the finite‐time H∞$$ {H}_{\infty } $$ control problem for a type of discrete‐time semi‐Markov jump systems (SMJSs) with partial unavailable information. A mode‐dependent resilient state feedback control strategy and the incomplete semi‐Markov kernel (SMK) method are applied to stabilize the obtained closed‐loop systems to protect against additive disturbances that can easily occur in the controller. By considering the upper and lower thresholds of sojourn time for each mode, the number of jumps of SMJSs is effectively estimated and new finite‐time bounded related criteria are established, which cover the general case of some previous studies and are more practical in depicting systems. Besides, the H∞$$ {H}_{\infty } $$ performance is further discussed and optimization problems are presented to achieve better closed‐loop performance. At last, a simulation example and a practical example are exhibited to reveal the validity of our raised control strategies and theoretical results. [ABSTRACT FROM AUTHOR]