Finite-Time Guaranteed-Cost H∞ Control of Time-Varying Systems With Actuator Saturation Based on Memory Dynamic Event-Triggered Mechanism

The problem of finite-time guaranteed-cost
$H_{\infty } $
control is studied for time-varying systems with actuator saturation using a memory dynamic event-triggered mechanism. By means of the dead-zone nonlinearity and the memory-based feedback controller, a guaranteed-cost function (GCF) considering actuator saturation and memory feedback data packets is constructed. A memory dynamic event-triggered mechanism is proposed, considering the historical transmitted data packets and a dynamic event-triggered threshold, and it can achieve a balance between saving network resources and maintaining the system performance. Furthermore, based on the constructed time-varying Lyapunov functional and the finite-time stability theory, sufficient conditions for guaranteeing
$H_{\infty } $
finite-time boundedness of the closed-loop time-varying system are given. These conditions also provide the upper bound of the GCF. By virtue of the interpolation formula, tractable recursive linear matrix inequality (RLMI) conditions are proposed to obtain the desired memory-based controller gains and event-triggered weighting matrix. Moreover, an RLMI-based algorithm is given to obtain the optimal values of GCF’s upper bound, finite-time stability and
$H_{\infty }$
performance index. Finally, the feasibility and superiority of the method are verified by a simulation example.