Stability and stabilization of systems with a cyclical time-varying delay via delay-product-type looped-functionals

In this paper, the stability analysis and synthesis of systems with a cyclical time -varying delay are investigated. At first, the entire delay interval is divided into intervals of monotonically increasing and monotonically decreasing alternating cycles. Then, a Lyapunov-Krasovskii functional (LKF) with two delay -product -type looped-functionals is constructed based on different delay monotone intervals. For the generated quadratic function with respect to delay in the derivative of LKF, a matrix -injection -based method is utilized to obtain the negative -definite conditions of LKF's derivative. A delay -dependent stability criterion with less conservatism is derived and the corresponding state -feedback control strategy is given consequently. Finally, a numerical example is utilized to show the superiority and the effectiveness of the proposed method, and a single -area power system under load frequency control is applied to verify the feasibility of the proposed control strategy.