We present a novel linear observer with an extension dealing with polytopic uncertainties in a vehicle dynamic system to identify the side-slip angle. The performance optimization issue is addressed by the minimization ofH∞norm of the system considering the estimation error as an output and the steer angle as an input. Contrary to the standard robust optimal design approaches, we use a convex inner approximation technique to reduce the order of the observer and this enables us to derive suboptimal, fixed-order, and efficiently practicable estimators. Moreover, the numerical examples performed on two-track nonlinear model of the system are provided to illustrate the impacts of design parameters on the optimization results and the efficiency of the technique.
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