Interval state estimation for uncertain polytopic systems

Abstract : The aim of this article is the state estimation of uncertain polytopic dynamic systems. The parametric uncertainties affecting the system are time varying, unknown and bounded with known bounds. The objective is to determine the state estimates consisting in the smallest interval containing the real state value caused by the parametric uncertainties. This set will be characterized by the lower and upper bounds of the state trajectory. Given the uncertainty bounds, the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a Luenberger-type observer, fed with the system measurements. The proposed observer is designed to minimize the interval width of the estimates. The observer gains are obtained by solving an optimization problem under LMI constraints. The efficiency of the proposed approach is illustrated by numerical examples.