Event-based control for discrete-time linear systems: design by emulation.
Event-based control, LPV systems, Control Design, Lyapunov Theory.
This work investigates the event-based control problem for discrete-time linear systems, encompassing precisely known systems and systems with time-varying parameters (Linear Parameter-Varying, LPV, systems). In network-controlled systems, it is desirable to save network resources. Thus, event-based control emerges as a strategy to reduce the transmission of control signals and avoid network overload. For precisely known systems, the design was performed through emulation with conditions formulated as Linear Matrix Inequalities (LMIs) and pre-determined control law. Different strategies were employed to trigger the control law to optimize the number of events. Optimization conditions were proposed to maximize the time interval between events. In the case of LPV systems, a potential issue arises regarding the periodic transmission of parameters alongside the control signal, which can lead to excessive data transmission and process inefficiency. An alternative approach was suggested by modifying the polynomial degree of the Lyapunov function and the controller, where a more robust controller tends to reduce event occurrences. Furthermore, the proposed emulation design for LPV systems used two different control laws obtained in the literature. Numerical simulations demonstrate the effectiveness of this approach in providing system stabilization conditions and event reduction.