© The Institution of Engineering and Technology
This study concerns the existence and design of reducedorder controllers for a rather general class of continuous and discretetime control design problems which can be characterised by the linear matrix inequality (LMI) framework. From a matrix pencil perspective, this paper presents a unified bound on the order of controllers in terms of the minimal rank of two matrix pencils valued at their generalised eigenvalues at infinity and in the unstable region (the closed righthalf plane for continuoustime systems and the region excluding the open unit circle for discretetime systems). When fullorder controllers exist, such matrix pencil characterisationbased bound reveals the existence of reducedorder controllers if one of two subsystems of the generalised plant has infinite zeros or unstable invariant zeros. A numerical example of obtaining reducedorder controllers for the covariance upper bound control problem is given. This study provides a more complete view of the role of infinite zeros or unstable invariant zeros in feedback systems.
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