In this paper, a new approach is suggested for asymptotic stabilization of a class of nonaffine quadratic polynomial systems in the presence of uncertainties. The designed controller is based on the sliding mode (SM) technique. This technique is basically introduced for nonlinear affine systems and in facing with nonaffine systems; attempts have been made to transform the system into an affine form. Lake of robustness is the main problem of the transformation approach. In this paper, a simple but effective idea is suggested to stabilize a system in its nonaffine structure and, therefore, a nonrobust transformation is not needed. In the proposed method, according to upper and lower bounds of uncertainties, two quadratic polynomials are constructed and with respect to the position of the roots of these polynomials, a new SM controller is proposed. This idea is also used for robust stabilization of a practical nonaffine quadratic polynomial system (magnetic ball levitation system). Computer simulations show the efficiency of the proposed control law.

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Abstract-Initial alignment in the presence of large misalignment angles is a critical issue in strapdown inertial navigation systems. The large initial misalignment angle adversely affects the accuracy and rapidness of the alignment process. In this paper a novel robust alignment approach is proposed based on a generalized proportional-integral-derivative filter. The proposed alignment approach has some significant advantages compared to the standard Kalman filter based alignment method. This method increases the accuracy and the convergence speed of the alignment process in the large misalignment angles problem. Experimental results also, verify the prominent performance of the presented approach in comparison to conventional standard Kalman filter based alignment method.

This paper considers the robust output tracking problem for a class of uncertain non-affine systems. The state-space equations of these systems have a non-affine quadratic polynomial structure. In order to design the output tracking controller, first the error dynamical equations are constructed. Then, a novel sliding mode controller is designed for robust stabilization of the error dynamical equations. For this purpose, a proper sliding manifold which is a function of error vector is suggested. According to upper and lower bounds of uncertainties, two quadratic polynomials are built and with respect to the location of the roots of the given polynomials, the new sliding mode control law is obtained. The proposed controller can conquer the uncertainties and guarantees the asymptotic convergence of the system output toward the wanted time-varying reference signal. Finally, in order to verify the theoretical results, the proposed method is applied to the magnetic ball levitation system. Computer simulations demonstrate the efficiency of the proposed method.

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