Stability and H₂ objective characterizations in control: A comparative study

This paper is concerned with stability and H₂ objective characterizations in control. New forms of alternative LMI characterizations are presented for continuous-time stability and H₂ objective. A key relationship between the alternative characterizations for continuous-time systems and the existing discrete-time versions is illustrated. The existing enhanced LMI characterization for continuous-time systems, called the reciprocal projection lemma, is revisited and an alternative proof is provided with a new interpretation. An -embedded LMI characterization is presented for a comparative study with the reciprocal projection lemma and for numerical analysis on the conservativeness of synthesis conditions. Through an application in control, it is discussed that, when applied to multi-objective problems in control, the alternative characterizations in this paper lead to an LMI solution with further significant conservativeness reduction, compared to the reciprocal projection lemma. In addition, through the comparison with the existing dilated LMI condition, it is shown that the dilated condition is an equivalent continuous-time counterpart of the existing discrete-time versions.