On absolute stability of sampled-data control systems

A problem is stated in the language of sequences which is equivalent to that of absolute stability of sampled-data control systems in the range of nonstationary nonlinearities which satisfy sectoral constraints. An algorithm is described for approximate determination of the Lyapunov indicator of a sampled-data system of this kind. Absolute stability of a sampled-data system is proved to be equivalent in the ranges of stationary and nonstationary nonlinearities which satisfy sectoral constraints. Conditions in plain terms of the transfer functions are provided that are necessary and sufficint for extendibility of the Tsypkin criterion.