Fixed Low-Order Controllers Achieving Comprehensive Admissibility and H∞ Performance

This paper presents primarily some new parametrizations of all static output-feedback controllers achieving admissibility or H
_∞
performance for linear timeinvariant descriptor systems. The parametrizations in question are in terms of a positive definite matrix and a generalized definite negative matrix and is rooted in the geometry of stable matrices set in state-space case. These parametrizations contribute to explicitly exhibit the whole structure of controllers, with fixed low-order, achieving comprehensive H
_∞
performance for a descriptor system control design under unstable and nonproper weights. An alternating projections based algorithm is proposed to solve such control design problem. An example is given to illustrate the efficiency of the proposed technique.