Robust Fixed-order Dynamic Output Feedback Controller Design for Delayed Vehicle Active Suspension System with Polytopic Uncertainty

In this paper, a fixed-order procedure is presented utilizing convex optimization and linear matrix inequalities (LMIs) to control a quarter car uncertain active suspension system. Our purpose is to design a low-order robust controller that keeps the desired design specifications besides the simplicity of the implementation. In our model, the system is influenced by the non-linear disturbance of the road surface, and the polytopic uncertainty model for state matrices of the system is utilized to cover the uncertainties of the model and the delay caused by the dynamic of the system. In this paper, a specific form of a positive definite matrix is used to overcome the complexity of rank minimization constraints. The proposed controller is considered with the most general statespace representation of linear systems which can be resulted by solving appropriate LMI constraints utilizing available efficient solving methods. Our proposed controller benefits from the dynamic property, independency of all individual states of the system, being of arbitrary order, and robustness against model uncertainty simultaneously. Eventually, a simulation example is presented to illustrate the correctness and effectiveness of the proposed method and obtained results for different orders that are compared with each other and also with that of a similar full-order method.