Abstract
This paper proposes a method to find super-stabilizing controllers for discrete-time linear systems that are consistent with a set of corrupted observations. The L-infinity bounded measurement noise introduces a bilinearity between the unknown plant parameters and noise terms. A super-stabilizing controller may be found by solving a feasibility problem involving a set of polynomial nonnegativity constraints in terms of the unknown plant parameters and noise terms. A sequence of sum-of-squares (SOS) programs in rising degree will yield a super-stabilizing controller if such a controller exists. Unfortunately, these SOS programs exhibit very poor scaling as the degree increases. A theorem of alternatives is employed to yield equivalent, convergent (under mild conditions), and more computationally tractable SOS programs.
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