A refined discretized timer-dependent Lyapunov functional for impulsive delay systems (Extended Version) ⋆

A new type of discretized Lyapunov functional is introduced for stability and hybrid L2 × l2-gain analysis of linear impulsive delay systems. This functional consists of three parts. The first part is the conventional discretized functional for delay-independent stability analysis. The second part is the looped-functionals-like functional for exploiting the internal structure inside impulse intervals, in which the decision matrix functions are approximated by piecewise linear matrix functions. The third part is a discretized adjustive factor, which makes the proposed Lyapunov functional continuous along the system trajectories. Thanks to this continuity, the resultant criteria for exponential stability and finite hybrid L2 ×l2-gain are expressed in terms of a combination of the continuous and discrete parts of the system. It is shown through numerical examples that the accuracy of the stability test increases with the increase of the partition number on impulse intervals, and the convergence rate is faster than that of the previous discretized functionals-based approach.