Finite-gain L ∞ stability from disturbance to output of linear delay systems via impulsive control

This study studies how impulses affect the bounded behaviours of delay system with bounded disturbance. By employing the method of Lyapunov function, several criteria of finite-gain L ∞ stability from disturbance to output are established. It is shown that a linear delay differential system can be finite-gain L ∞ stabilised from disturbance to output using impulsive feedback control even there is an unstable matrix. Moreover, delay differential equations also maybe finite-gain L ∞ stable from disturbance to output under an appropriate sequence of impulses treated as disturbances. Two examples and simulations are also given to illustrate our results.