Parametric Lyapunov Equation Based Event-Triggered and Self-Triggered Control of Discrete-Time Linear Systems

This paper is considered with semi-global stabilization of discrete-time linear systems subject to actuator saturation based on event-triggered control (ETC) and self-triggered control (STC). First, a novel ETC algorithm is proposed by utilizing properties of the discrete-time parametric Lyapunov equation. Moreover, the corresponding STC, in which the next control law depends on the previous triggered states, is designed to avoid continuous monitoring system states. The designed control algorithms not only save energy but also provide a very clear relationship between the only design parameter and the minimal inter-event time, which can be easily used to change regularly inter-event times (IET) by adjusting the only design parameter and allows us to find easily a tradeoff between IET and the control performance. Finally, the designed ETC and STC are used to stabilize the inertia wheel pendulum system. Numerical simulations show the effectiveness of the proposed algorithms.