On reachable set estimation of delay Markovian jump systems with partially known transition probabilities

In this paper, the problem of reachable set estimation of discrete-time Markovian jump systems with time-varying delay is addressed. By applying the improved reciprocally convex combination approach to bound the forward difference of double summation and the reciprocally convex combination approach to bound the forward difference of triple summation, a sufficient condition on reachable set estimation is first derived for delay Markovian jump systems with completely known transition probabilities. Then the result is extended to delay Markovian jump systems with partially known transition probabilities. Based on the criterion, a less conservative stability criterion for delay Markovian jump systems is also obtained as a by-product. In order to illustrate the effectiveness and the reduced conservatism of the proposed results, three numerical examples are presented.