Parameter dependent Lyapunov functions for robust stability of time-varying linear systems under point delays

Abstract This paper investigates the stabilization dependent on the delays of, in general, time-varying linear systems with multiple constant point time-delays. The matrices describing the state-space dynamics are parameterized by, in general, time-varying function matrices governed by coefficient functions in compact sets. The closed-loop sufficiency-type stability conditions are obtained from Lyapunov’s stability theory by constructing parameter-dependent candidates which satisfy, in the most general case, a Riccati matrix differential inequality.

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