Abstract
Linear quadratic regulators are in certain sense known to possess considerable amount of robustness margins. This paper is concerned with optimality robustness problems for single-input quadratic regulator systems with parameter uncertainties. The uncertainties are assumed to take on value in prescribed intervals. We show that Kharitonov-type extreme point results hold for two kinds of parameters:the coefficients of the open-loop characteristic equation and the elements of the designed optimal feedback gain vector. In both cases, optimality at a few extreme parameter values ensures that property at whole range of parameter values. These are derived from known results in the inverse problems of optimal regulators which for single input case feature geometric interpretations in particular. Numerical examples are provided to illustrate these extremal results.
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