Applied Physics and Mathematics Annotation << Back lyapunov function for nonlinear continuous control systems with a periodic linear part Morozov M.V. We consider nonlinear continuous control systems with a periodic linear part and equivalent periodic differential inclusion of a special form. Equivalence is meant in the sense of coincidence of the sets of solutions of systems and the inclusion under the same initial conditions. It is shown that uniform absolute stability in the class of systems under discussion occurs if and only if there exists a single time-periodic Lyapunov function of quasiquadratic form. This result is generalized to the case of periodic differential inclusion of a special form. The nonstationary Lyapunov function which was constructed is locally Lipschitzian, time-periodic, convex with respect to vector characterizing the deviation of the system from the mode taken to be the target of control, and, generally speaking, is not continuously differentiable with respect (t, x), which is usually assumed in classical Lyapunov theorems for the nonstationary case. For this reason generalized derivative for the Lyapunov function for the system under consider or for the differential inclusion, which is equivalent to the system, was utilized. Estimates of chosen Lyapunov function were obtained which garantize the properties of positive definiteness and the existence of an infinitesimal upper limit. Keywords: absolute stability criteria, nonlinear continuous control systems, uniform absolute stability, uniform exponential absolute stability, Lyapunov function. Contacts: E-mail: miguel@ipu.ru Pp. 66-72.