Exponential stability analysis for linear distributed parameter systems with time-varying delay

This paper investigates exponential stability of time-delay distributed parameter systems in the Hilbert space. With the aid of delay decomposition methods, a novel Lyapunov-Krasovskii functional in the form of linear operator inequalities (LOIs) is proposed. Then, the sufficient conditions guaranteeing exponential stability of systems are obtained by the Lapunov-Krasovskii theory. Furthermore, our results are applied to the time-delay heat equation with the Dirichlet boundary condition. A numerical simulation to the heat equation is given to illustrate the effectiveness of the theoretical analysis.