Mathematical Problems in Engineering 
Volume 6 (2000), Issue 5, Pages 411-424
doi:10.1155/S1024123X0000140X

Window observers for linear systems

Vadim Utkin and Shengming Li

 Department of Electrical Engineering, The Ohio State University, 205 Dreese Lab, 2015 Neil Avenue, Columbus 43210, OH, USA
Received 18 December 1999; Revised 13 January 2000

Abstract

Given a linear system x˙=Ax+Bu with output y=Cx and a window function ω(t), i.e., ∀t,ω(t)∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, xˆ=Ax+Bu+ω(t)LC(x−xˆ) as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications