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 $H_{\infty }$ performance for linear time-invariant 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 $H_{\infty }$ performance for a descriptor system control design under unstable and non-proper 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.