A Parameter-Dependent Approach to Observer-Based Control for Networked Control LPV Systems

We address the observer-based controller design problem for networked control LPV (NC LPV) systems, which are network-based systems that depend on unknown but measurable time-varying parameters. According to the analysis of the special issues brought by introducing network into LPV systems and the state reconstruction based on the observer, a new augmented model is established with two independent time-varying delays, which can carry out the controller and observer collaborative design effectively. Based on the parameter-dependent Lyapunov stability theory, a sufficient condition is proposed to ensure that the closed-loop system is asymptotically stable with a guaranteed performance level γ, in which the coupling between Lyapunov function matrices and the system matrices existed. By using the Projection Lemma and introducing a slack matrix, the decoupling is achieved successfully, which refers to reducing conservatism. In the present study, the condition for stability analysis and control synthesis is formulated in terms of the parameterized linear matrix inequality (PLMI), which is infinite-dimensional and can be transformed into finite by using the basis function method and gridding technique. A numerical example is given to demonstrate the high validity and merit of the proposed approach.