Invariant Sets and Guaranteed Cost Control of Nonlinear Quadratic Systems

This paper addresses the problem of designing a guaranteed cost controller for continuous-time nonlinear quadratic systems. The main result is a sufficient condition for the existence of a linear state feedback controller achieving an assigned guaranteed cost, whenever the state trajectories remain within a suitable invariant set. The conditions are cast in the form of Linear Matrix Inequalities (LMIs), which can be efficiently solved via available optimization algorithms. The effectiveness of the devised approach is illustrated through an example concerning the attitude control of an unmanned aerial vehicle.