Linearly Combining Sensor Measurements Optimally to Enforce an SPR Transfer Matrix

Abstract

This paper presents methods to combine measurements of a linear time-invariant system in such a manner that the new system obtained is strictly positive real (SPR). In particular, this paper focuses on how to best combine measurements in a linear fashion by minimizing the difference in an $\mathcal{H}_{2}$ or $\mathcal{H}_{\infty}$ sense between the new system and a given desired system. The methods proposed to linearly combine sensor measurements rely on linear matrix inequalities (LMIs), which lead to tractable synthesis procedures. Numerical examples involving noncolocated elastic mechanical systems are provided that illustrate the effectiveness of the proposed techniques when used for output tracking control.