Passivity analysis of Markov jump BAM neural networks with mode-dependent mixed time-delays via piecewise-constant transition rates

Passivity problem is studied for Markov jump bi-directional associative memory (BAM) neural networks with both mode-dependent mixed time delays and time-varying transition rates. In this paper, we consider both discrete delay and distributed delay which are all switching based on Markov process r(t). Time-varying transition rates are, respectively, discussed under the cases of known transition rates and partly unknown transition rates. The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant. By utilizing LMIs technique and a class of Lyapunov functionals, a switching delay passivity criterion underlying known transition rates is derived, which can be easily checked by the Matlab LMI Tool Box. Furthermore, we extend the result to passivity analysis of Markov jump BAM neural networks with partly unknown transition rates. The results obtained relate on not only switching discrete delays but also switching distributed delays. Finally, a numerical example is given to illustrate the effectiveness of the results.