Event-triggered sampled-data control of oscillatory systems.

ABSTRACT:
The talk is mainly devoted to sampled-data control of a class of Lurie systems where the sampling time sequence is generated by continuous event-trigger. Such systems describe, in particular, many oscillator control models, for example, pendulum-like systems. The problem is the proper choice of the sampling interval providing exponential stability and the desired performance of the control system. The proposed approach exploits E. Fridman’s method based on a general time-dependent Lyapunov–Krasovskii functional. With classical results of V. A. Yakubovich on S-procedure, the problem is reduced to feasibility analysis of linear matrix inequalities.
The talk also covers the problem of the network-based energy control of one-degree-of-freedom Hamiltonian systems. This problem is nontrivial since the control objective is stabilization of an invariant manifold in phase space. As the nominal feedback law, the speed gradient method is used. The effect of a certain network imperfection (sampling, quantization, and time-delay) is represented as an additional input error. However, in the presence of even a sufficiently small input error, a Lyapunov function may not always decrease which creates extra difficulties for analysis. More delicate calculations allow to conclude that the time periods on which it may increase and the amount by which it may increase are suitably bounded and decreasing behavior still dominates. Using these properties, one can establish that if the initial energy level is not too far from the desired one, then it will remain not too far from it and will eventually become close to it. While this result may appear intuitively not surprising, the main contribution lies in precisely characterizing allowed network imperfection bounds and resulting energy deviation bounds.