Lyapunov-Krasovskii Functional with Prescribed Derivative and Lyapunov Matrix for Delay System with Distributed Parameters

The method of Lyapunov-Krasovskii functionals is widely used to study stability and robust stability. An important part of this method is the construction of the Lyapunov functional matrix. In this paper we consider time-delay equation with distributed parameters. An explicit form of the functional with prescribed derivative is presented. The basic properties defining the Lyapunov matrix are found and its explicit form is presented for the case of an exponentially stable system.