Dynamic periodic event-triggered gain-scheduling control co-design for quasi-LPV systems

Abstract

This paper investigates dynamic periodic event-triggered gain-scheduling control co-design for nonlinear systems subject to disturbances. The considered class of nonlinear systems is such that an equivalent polytopic quasi-LPV model is obtained. Based on the co-design approach, gain-scheduled control law and dynamic event-triggering mechanism (ETM) are jointly designed. The proposed co-design condition is formulated in terms of linear matrix inequality (LMI) conditions which are derived from the Bessel–Legendre inequality and the delay-dependent reciprocally convex combination lemma. As the state information is available to the gain-scheduled controller at specific instants determined by the ETM, it induces the asynchronous phenomenon between the parameters of the controller and the plant’s quasi-LPV model. To reduce the conservativeness induced by this asynchronous phenomenon, an LMI relaxation is proposed. Numerical examples illustrate the advantages of the proposed dynamic periodic event-triggered control co-design approach over its static counterpart.