Descent ILMI Algorithm for ${\mathbb {D}}^{\prime }$-${\mathbb {D}}^{\prime \prime }$ ${\mathscr {H}}_{\infty} ^{\mathbb {B}}$-Controller

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Abstract
The problem of obtaining a dynamic controller such that its poles and the modes of the closed-loop (CL) system are in specified regions ${\mathbb {D}}^{\prime}$ and ${\mathbb {D}}^{\prime \prime }$ in the open left complex half-plane, such that the CL transfer matrix has as small as possible norm over a prescribed frequency range ${\mathbb {B}}$ is considered. A novel optimization algorithm for controller design is presented. The algorithm is based on iterative solving linear matrix inequalities and finds in every iteration a minimal norm static output feedback control for a descriptor system. A problem solution is obtained in every iteration, while the performance index decreases. A formal proof that the algorithm is descent in respect to the performance index is given for some subproblems.

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