Asynchronous finite-time H∞ control of discrete-time switched systems: An inverse weighted switching scheme

The work proposes an asynchronous convex Lyapunov function and an inverse weighted switching scheme to study the asynchronous finite-time H∞ control issue of discrete-time switched systems. Based on the manipulation that the switching interval is partitioned into three sections, the designed Lyapunov function is constructed in convex structure, reducing the conservatism caused by the low degree of freedom. Owing to the finite-time parameter, the inverse weighted form of the dwell time can be used to characterize the exponent term. The inverse weighted switching is raised to erase the dwell time restriction of each subsystem, only requiring that the inverse weighted sum of all dwell times is less than a constant. Based on the asynchronous convex Lyapunov function and inverse weighted switching, the l2-gain analysis is conducted to derive the asynchronous finite-time H∞ controller. Finally, two numerical examples and an application example are given to verify the potential and validity of the proposed results.