State-feedback control for continuous-time LPV systems with polynomial vector fields

This paper is concerned with the design of state-feedback controllers for Linear Parameter Varying (LPV) polynomial continuous-time systems. The vector field presents polynomial dependence on the states. Two synthesis conditions are proposed, the first one considers arbitrary rates of variation in the time-varying parameters, while the second one provides LPV controllers that are constructed based on a smoothed approximation of the time-varying parameter. The sum of squares matrix decomposition is employed to solve the proposed conditions. The L2 gain is also considered to give a robustness measure of the proposed controllers. The results are illustrated with examples from the literature.