Window observers for linear systems
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 pro...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2000-01-01
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| Series: | Mathematical Problems in Engineering |
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| Online Access: | http://dx.doi.org/10.1155/S1024123X0000140X |
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doaj-6b4c612d12cf4b8bb5f321c887dcf1f52020-11-24T23:12:04ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472000-01-016541142410.1155/S1024123X0000140XWindow observers for linear systemsVadim Utkin0Shengming Li1Department of Electrical Engineering, The Ohio State University, 205 Dreese Lab, 2015 Neil Avenue, Columbus 43210, OH, USADepartment of Electrical Engineering, The Ohio State University, 205 Dreese Lab, 2015 Neil Avenue, Columbus 43210, OH, USAGiven 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 applicationshttp://dx.doi.org/10.1155/S1024123X0000140XObserver; Stability; Windowing function. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Vadim Utkin Shengming Li |
| spellingShingle |
Vadim Utkin Shengming Li Window observers for linear systems Mathematical Problems in Engineering Observer; Stability; Windowing function. |
| author_facet |
Vadim Utkin Shengming Li |
| author_sort |
Vadim Utkin |
| title |
Window observers for linear systems |
| title_short |
Window observers for linear systems |
| title_full |
Window observers for linear systems |
| title_fullStr |
Window observers for linear systems |
| title_full_unstemmed |
Window observers for linear systems |
| title_sort |
window observers for linear systems |
| publisher |
Hindawi Limited |
| series |
Mathematical Problems in Engineering |
| issn |
1024-123X 1563-5147 |
| publishDate |
2000-01-01 |
| description |
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 |
| topic |
Observer; Stability; Windowing function. |
| url |
http://dx.doi.org/10.1155/S1024123X0000140X |
| work_keys_str_mv |
AT vadimutkin windowobserversforlinearsystems AT shengmingli windowobserversforlinearsystems |
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1725602579617939456 |