Reachable set estimation for inertial Markov jump BAM neural network with partially unknown transition rates and bounded disturbances

Abstract

This paper mainly focuses on the reachable set estimation problem of a time-varying delayed inertial Markov jump bidirectional associative memory (BAM) neural network with bounded disturbance inputs. The disturbances are assumed to be either unit-energy bounded or unit-peak bounded. Different from systems of the past studies, this paper is for inertial Markov jump BAM neural network with both time-varying delay and time-varying transition rates. The time-varying character of the considered transition rates is assumed to be piecewise-constant. In order to reduce the conservatism, the delay-partitioning technique is utilized to solve this reachable set estimation problem. As a result, it is obtained that the ellipsoid defined in this paper contains the reachable set Rup, which indicates the reachable set Rue is included. Further, we extend the results to the uncertain Markov jump BAM neutral network with partially unknown transition probabilities. Numerical examples are proposed to show the effectiveness of the given results.