Time-limited model reduction for semi-markovian jump systems based on generalized gramians

This paper is concerned with the approximation problem for semi-Markovian jump systems (SMJSs) based on generalized time-limited Gramians. For a given SMJS with partially known transition probabilities, the generalized time-limited Gramians are defined and then solved by using time-interval input/output energy functions. The proposed model reduction algorithm can solve the synchronization jump problem, and also achieve the required reduced accuracy within the expected time-interval. Specially, the reduced error of the proposed algorithm is lower compared with the balanced truncation method, which has more theoretical value in time-interval control synthesis. Finally, a numeral example including four subsystems is given to estimate the effectiveness of the proposed results.