Observer-Based Controllers for Incrementally Quadratic Nonlinear Systems with Disturbances

Abstract

This paper investigates observer-based output feedback control design for incrementally quadratic nonlinear systems with bounded external disturbances. The nonlinearities considered satisfy incremental quadratic constraints, which are characterized by incremental multiplier matrices and include many common nonlinearities as special cases. Linear matrix inequality (LMI) conditions are presented to separately construct the continuous-time observer and the feedback control law for two parameterizations of the incremental multiplier matrices. The observer and the controller gains are obtained from the LMI solutions and proved to render the closed-loop system inputto-state stable with respect to external disturbances. Based on the continuous time observer-based controller designed, eventtriggered controllers with Zeno-freeness are constructed for two triggering configurations where the first one implements the event-triggering mechanisms (ETMs) in the controller-toactuator channel and the second one implements ETMs in both the controller-to-actuator channel and the sensor-to-observer channel asynchronously. For each configuration the closed-loop system is proved to be input-to-state practically stable. The theoretical results are illustrated via simulations of a single-link robot arm example.