Analysis of time-varying control strategies for optimal disturbance rejection and robustness

Analysis of linear time-invariant systems that are controlled by time-varying controllers is given. The problems of disturbance rejection and robustness are formulated and analyzed using functional analytic methods, which reveal the properties that are common to these problems. The theoretical development presented uses the theory and techniques of nuclear operators and their relation with the duality theory of tensor products of Banach spaces. The authors show how time-varying compensation offers no advantage over time-invariant compensation for the problem of disturbance rejection over general signal spaces, in both continuous and discrete time, and for the problem of L_∞ robust stabilization of time-invariant plants. In addition, another application of the theory for the problem of norm minimization subject to a norm constraint is presented