Stabilization of a scalar equation with delay in the state and control variables

The contribution is dedicated to the stabilization problem of systems with input and state delay. We derive a stabilizing control law for the case of a scalar equation with several state and two input delays. We start with a control law of the form, where the right hand side contains future values of the state predicted by Cauchy formula. The presented control law is of the form of an integral equation. It is shown that the characteristic function of the closed-loop system consists of two factors. Special conditions that guarantee the exponential stability of the closed-loop system are derived. Exponential estimates for the solutions of the closed-loop system are given. An illustrative example is presented. Bibliogr. 9.