Interval Estimation for Time-Varying Descriptor Systems via Simultaneous Optimizations of Multiple Interval Widths
Zhenhua Wang, Youdao Ma, Qinghua Zhang, Wentao Tang, Yi Shen
Abstract
This article investigates the state interval estimation problem for discrete-time linear time-varying descriptor systems subject to unknown but bounded system uncertainties. We propose a zonotope-based interval estimation method in an optimization framework. First, we present a novel zonotope-based interval estimator structure, in which the estimated interval bounds of each state component have design parameters independent of those of the other state components. Then, the widths of the jointly estimated intervals enclosing every state component are simultaneously minimized by solving parallel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$</tex-math> </inline-formula> optimization problems via linear programming. Finally, a simulation study shows the effectiveness and higher accuracy of the proposed method compared with existing methods.