The Barycentric Bernstein Form for Control Design

In this paper, an algorithm for computing a polynomial control and a polynomial Lyapunov function in the simplicial Bernstein form is developed. This ensures asymptotic stability of the designed feedback system. To this end, we provide certificates of positivity for polynomials in the simplicial Bernstein form. Subsequently, the state space is partitioned into simplices. On each simplex, we simultaneously compute Lyapunov and control functions. With this control, the equilibrium is asymptotically stable.

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