Guaranteed cost control via optimal parametric LQ design

For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closed-loop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system obtained by parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem, referred to as robust optimal parametric LQ control with a guaranteed-cost bound, is addressed. A design method is proposed for finding an optimal controller that simultaneously guarantees robust stability and performance over a specified range of parameter variations. A versatile numerical algorithm is given for computing the robust optimal gains. The usefulness of the design method is demonstrated by the design of robust control of a VTOL helicopter