On the digital event-based control for nonlinear time-delay systems with exogenous disturbances

Abstract

In this paper, the stabilization problem of nonlinear time-delay systems in presence of known exogenous disturbances and by means of quantized sampled-data event-based controllers is investigated. In particular, nonlinear systems with state delays are studied. Known exogenous disturbances affecting the plant dynamics are considered in order to address, for instance, tracking control problems commonly studied by considering the stabilization problem of the corresponding tracking error system in which the chosen reference signal appears as a known exogenous signal. The stabilization in the sample-and-hold sense theory is used as a tool to provide sufficient conditions for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the quantized sampled-data implementation of continuous-time controllers, updated through a proposed event-based mechanism, guarantees the semi-global practical stability property, with arbitrarily small final target ball of the origin, of the related closed-loop system. A spline approximation methodology is used in order to: (i) cope with the problem of the possible non-availability in the buffer of suitable past values of the system variables needed for the digital implementation of the controller; (ii) consider approximations related to the hardware implementation of the signal describing the known exogenous disturbance (e.g., the chosen reference signal). The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results, one of which concerning a single-link flexible joint robot arm with time delays.