Robust regulation with H(2) or H(infinity) performance

In this thesis, three performance problems in linear control systems are studied. Robust regulation against steps and sinusoids is the first. Major results on this classic problem are rederived using only basic state-space ideas.The second problem studied is that of minimizing the ${\cal H}\sb2$ norm of a feedback system--the classic LQG problem--subject to the constraint that the controller also solve the robust regulation problem. It is shown that the requirement of robust regulation results in, at most, an arbitrarily small penalty in terms of increased ${\cal H}\sb2$ norm. Necessary and sufficient conditions are also derived that indicate exactly when there exists a controller that both robustly regulates and achieves the optimal ${\cal H}\sb2$ norm. All proofs are constructive.The third problem studied is that of achieving a given ${\cal H}\sb{\infty}$ norm, subject to the constraint that the controller also solve the robust regulation problem. This problem can also be interpreted as a robust performance problem: find a controller that solves the robust regulation problem for every plant determined by an unstructured, norm-bounded uncertainty block. It is shown that this problem admits a solution if and only if the ${\cal H}\sb{\infty}$ problem is solvable and certain matrix inequalities are satisfied, one inequality for every frequency that is robustly regulated against. Controller synthesis is addressed.U of I OnlyETDs are only available to UIUC Users without author permissio