An LMI-based unified approach to reduced-order controller design
The design of reduced-order controllers is considered for stabilization control, covariance upper bound control, linear quadratic regulator, \({\mathcal L}_\infty\) control, \(H_\infty\) control, positive real control problems and robust \(H_2\) control, robust \({\mathcal L}_\infty\) control and robust \(H_\infty\) control problems for generalized linear plants without any additional assumptions. An upper bound of the order is obtained with which the (robust) controllers can guarantee stability constraints and satisfy the same design objectives as the so-called ``full-order'' controllers. A unified linear-matrix-inequality (LMI) based approach to reduced-order (robust) controller design for all the above-mentioned problems is provided. It is shown that each of these problems is solvable if and only if two uncoupled LMIs with an LMI-type constraint have a pair of positive definite solutions, one of which has a lower dimension than the one given by Skelton and Iwasaki (1995). All desired reduced-order (robust) controllers are parametrized via the solutions of the LMIs. Moreover, a design procedure is proposed based on the above LMI approach.
scientific article; zbMATH DE number 1150131