Finite-Time Stabilization of Linear Systems With Unknown Control Direction via Extremum Seeking

In this article, the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting modified version of classical extremum-seeking algorithm. We propose to use suitable oscillatory input modify dynamics, at least in an average sense, so as satisfy differential matrix inequality condition, which turn guarantees that system’s state remains inside prescribed hyperellipsoid space. The stability (FTS) averaged dynamics implies FTS original system, distance between and can be made arbitrarily small choosing sufficiently high value dithering frequency used main advantage proposed approach resides its capability dealing systems direction, and/or changes over time. Being quantitative approach, article also gives estimate necessary minimum dithering/mixing provided, effectiveness analyzed means numerical examples.