Linear Time-Invariant System Reduced-Order Finite-Time Observer

Abstract

AbstractDue to its excellent estimation performance and great application value, finite-time observers have attracted more and more scholars' attention in recent years. Compared with traditional asymptotic observers, finite-time observers not only have fast convergence speed, but also have high estimation accuracy. However, the classical method only discusses the full-order finite-time observer, and the research on the reduced-order finite-time observer has not been reported. To this end, this paper considers the design of a reduced-order finite-time observer for a class of linear time-invariant systems. First, a new state transformation method is proposed so that the transformed partial state can be represented by the measured output, and a finite-time observer is designed for another unmeasurable partial state to estimate it. According to this idea, it is proved that the observability condition required in the classical full-order finite-time observer design can also guarantee the existence of a reduced-order finite-time observer. Finally, a numerical example is given to verify the effectiveness of the proposed method.KeywordsFinite-time observerReduced-order observerObservability condition