Further Results on the Input-to-State Stability of a Linear Disturbed System with Control Delay

Abstract

In this paper, a theorem is obtained that gives sufficient input-to-state stability conditions for linear systems with control delay and additive disturbances. Stabilizing feedback is considered available in the absence of delay and disturbances. The mathematical tools are the Lyapunov–Krasovskii functional, the Jensen inequality and the double Hadamard inequality. The critical delay is highlighted.

Keywords

• control delay
• input-to-state-stability
• Lyapunov–Krasovskii functionals
• linear disturbed systems
• critical delay