The state realization is called minimal if it is either accessible and observable or its state dimension is minimal. In the linear case those two definitions are equivalent, but not for nonlinear time-invariant systems. It is shown that definitions remain equivalent in case one is searching for minimal realization in a larger class of nonlinear time-varying systems. First, nonlinear realization...

Keywords: Systems of nonlinear delay differential equations Time-varying delays Global stability M-matrix BAM neural network Leakage delays a b s t r a c t We consider a nonlinear non-autonomous system with time-varying delays

This work is devoted to investigate the stability properties of time-delay reset systems. We present a Lyapunov-Krasovskii proposition, which generalizes the available results in the literature, providing results for verifying the stability of time-delay reset systems with nonlinear and time-varying base system. We demonstrate the applicability of the proposed results in the analysis of time-de...