STABILITY CONDITION OF DISTRIBUTED DELAY SYSTEMS BASED ON AN ANALYTIC SOLUTION TO LYAPUNOV FUNCTIONAL EQUATIONS

Abstract

An analytic solution to Lyapunov functional equations for distributed delay systems is derived. The analytic solution is computed using a matrix exponential function, while conventional computation has been relied on numerical approximations. Based on the analytic solution, a necessary and sufficient stability condition for distributed delay systems with unknown but bounded constant delay is proposed.