$H_{infty}$ Design with First Order Controllers
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This paper considers the problem of determining the complete set of first order controller parameters for which the frequency weighted Hnorm of some closed loop transfer function is less than a specified constant and the closed loop system is stable. The results apply to single-input single-output, linear, time invariant plants of arbitrary order. The problem of determining all first order controllers (C(s) = x1s+x2/s+x3) which stabilize such a plant has been recently solved in [10]. In this paper, these results are extended to determine the subset of controllers which also satisfy various robustness and performance specifications which can be formulated as specific Hnorm constraints. The problem is solved by converting the Hproblem into the simultaneous stabilization of the closed loop characteristic polynomial and a family of related complex polynomials. The stability boundary of each of these polynomials can be computed explicitly for fixed x3by solving linear equations. The union of the resulting stability regions yields the set of all x1and X2which simultaneously satisfy the Hcondition and closed loop stability for a fixed x3. The entire three dimensional set meeting specifications is obtained by sweeping x3over the stabilizing range.
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42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)
