Parametric Lyapunov equation based event-triggered and self-triggered control of input constrained linear systems

This article studies semiglobal stabilization of input constrained linear systems based on the static and dynamic event-triggered control (ETC) and self-triggered control (STC). First, a static ETC based on the parametric Lyapunov equation (PLE) is designed. Then the corresponding dynamic ETC is also proposed. The main advantage of the proposed static and dynamic ETC algorithms is that the minimum interexecution time (MIET) as a decreasing function of the parameter in the PLE is given, which allows us to find easily a trade-off between the interexecution times (IETs) and the control performance. The fact that the MIET of the dynamic ETC is never less than that of the static ETC is also guaranteed. Next, in order to avoid continuous monitoring of the states, both static and dynamic STC are designed. The influence of the parameters on IETs of the static and dynamic STC is analyzed in detail. The nonoccurrence of the Zeno phenomenon is proved in all the control algorithms. Finally, the proposed algorithms are applied to the design of spacecraft rendezvous. Numerical simulations on the original nonlinear model of the spacecraft rendezvous control system show the control system effectiveness of the algorithms.