Guaranteed H∞ Disturbance attenuation and l1 control and output bounds with LEB regulators

Most of the standard regulator solutions applicable to linear systems focus only on time-domain or frequency-domain results. Some techniques accommodate mixed-domain performance specifications providing solutions through the use of numerical optimization but do not give insight on the conditions under which such solutions exist or how to perform tradeoffs. The article presents a technique by which it is possible to find a regulator to make a linear system satisfy control and output l₁-norm bounds and, modifying them, to achieve a desired H_∞-norm of the disturbance-to-output transfer function. A linear-ellipsoidal-bounded formulation is involved. Also, frequency weightings are added to the input and states of the original plant to allow more flexibility in the frequency domain