Controller Design for Robust Stability and Performance

The closed loop system property (A+BG) ≪ 0 is important for robust stability and performance to errors in model parameters. This paper defines the set of all G such that (A+BG) ≪ 0 for a given A and B, and develops a strategy for choosing a particular gain from this set that satisfies the following objectives: (i) The root-mean squared (rms) value for each system state of the nominal system is less than or equal to some prespecified values for a given disturbance environment. (ii) The rms value for each state of the uncertain system is less than or equal to the same prespecified values in (i) for an a posteriori determined set of perturbations.