Stability with mixed H ∞/passivity performance analysis of fractional-order neutral delayed Markovian jumping neural networks

Abstract A detailed survey of existing works on fractional-order nonlinear systems reveals the fact that practically no results exist on stability or any performance analysis of Markovian jumping fractional-order systems (FOSs) in general. The main reason is the theory of infinitesimal generator used to estimate the derivative of Lyapunov–Krasovskii Functional (LKF) is not well-developed in the fractional domain. This shortage, in theory, is focussed in this manuscript. In this work, we provide a lemma that aids in analyzing the stability of fractional-order delayed systems via integer-order derivative of LKF. Using this lemma, by constructing a new suitable LKF and employing known integral inequalities, linear matrix inequality (LMI)-based sufficient conditions that ensure stability along with H ∞ /passive performance of the proposed fractional-order neural networks (FONNs) with Markovian jumping parameters are derived for the first time. Unlike the existing works, the results derived in the present study depend on the fractional order (FO) of the NNs. The importance of such order-dependent criteria is highlighted in numerical examples. Finally, the simulation results are given to show the reliability of the derived conditions.