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A Study on quadratic stability of optimal regulators under gain adjustment

The objective of this paper is to show an online adjustment method of the state feedback gains for multiinput multi-output optimal regulators via the quadratic stability arguments. We first give a region of state feedback gains containing the nominal optimal gain such that quadratic stability is ensured for all time-invariant state feedback gains in the region. We then show that under some mild conditions, quadratic stability is retained for arbitrary time-varying adjustment of the state feedback gain within this region via the concept of strong uniform complete observability.