Linear matrix inequality stability conditions from a parameter-dependent Lyapunov functional for linear systems with a time-varying delay

摘要

This paper proposes new stability conditions for linear systems with a time-varying state delay. The time-varying delay is treated as a polytopic uncertainty parameter, and a Lyapunov functional that is dependent on the delay parameter is constructed. Linear matrix inequality conditions of system stability and robust stability are derived. Numerical and practical examples are given to show the effectiveness and non-conservativeness of the proposed conditions.