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Extending Lyapunov redesign method for robust stabilization of non-aﬃne quadratic polynomial systems

Binazadeh T., Rahgoshay M.

Control and Cybernetics

2016

Vol. 45, no. 3

373--384

The Lyapunov redesign method is basically used for robust stabilization of nonlinear systems with an aﬃne structure. In this paper, for the ﬁrst time, by suggestion of a simple but eﬀective idea, this approach is developed for robust stabilization of non-aﬃne quadratic polynomial systems in the presence of uncertainties and external disturbances. In the proposed method, according to the upper bound of an uncertain term, a quadratic polynomial is constructed and with respect to the position of the roots of this polynomial, the additional feedback law is designed for robustness of the quadratic polynomial system. The proposed technique is also used for robust stabilizing of a magnetic ball levitation system. When the coil current is the control input of the magnetic ball levitation system, equations of this system are increasingly nonlinear with respect to control input and have quadratic polynomial structure. The effectiveness of the proposed control law is also demonstrated through computer simulations.