Control design and Lyapunov Functions via Bernstein Approximations: Exact Results. Issue 2 (2020) - Hamadneh, Tareq; Athanasopoulos, Nikolaos; Wisniewski, Rafael
Abstract: We study the control problem for polynomial continuous-time dynamical systems. We consider polynomial Lyapunov functions and controllers, both parameterised in Bernstein form. Specifically, we present necessary and sufficient conditions for existence of polynomial controllers and Lyapunov functions of some maximum degree, providing at the same time explicit upper bounds on the degree of the involved Bernstein polynomials. The formulated conditions are a set of algebraic inequalities, in the space of Bernstein coefficients.