We propose a pre-T event-triggered controller (ETC) for the stabilization of a chain of integrators. Our per-T event-triggered controller is a modified event-triggered controller by adding a pre-defined positive constant T to the event-triggering condition. With this pre-T, the immediate advantages are (i) the often complicated additional analysis regarding the Zeno behavior is no longer needed, (ii) the positive lower bound of interexecution times can be specified, (iii) the number of control input updates can be further reduced. We carry out the rigorous system analysis and simulations to illustrate the advantages of our proposed method over the traditional event-triggered control method.

This paper is a sequel to [4] in which the system is generalized by including unknown time-varying delays in both states and input. Regarding the controller, the design of adaptive gain is simplified by including only x1 and u whereas full states are used in [4]. Moreover, it is shown that the proposed controller is also applicable to a class of upper triangular nonlinear systems. An example is given for illustration.

For systems with a delay in the input, the predictor method has been often used in state feedback controllers for system stabilization or regulation. In this letter, we show that for a chain of integrators with even an unknown input delay, a much simpler and memoryless controller is a good candidate for system regulation. With an adaptive gain-scaling factor, the proposed state feedback controller can deal with an unknown time-varying delay in the input. An example is given for illustration.