The Lyapunov direct method is utilized to determine the
robustness bounds for nonlinear, time-variant uncertainies
p[subscript i]. Determination of the robustness bounds consists of two
principal steps: (i) generation of a Lyapunov function and
(ii) determination of the bounds based on the generated
Lyapunov function. Presently in robustness investigations,
a Lyapunov function is generated by inserting the nominal
matrix to the Lyapunov equation and setting Q as identity
matrix. The objective of this study is to utilize structural
features of the uncertainties to develop a recursive
algorithm for the generation of the globally optimal quadratic
Lyapunov function. The proposed method is seemingly
an improvement with respect to those reported in recent
literature in three senses: i) ease of application, given
an interactive program which requires only system matrices
as inputs; ii) provision of improved estimates of the
robustness bounds; and iii) extendability of the procedure
to the design of robust controllers. The algorithm and the
program prepared (in MATLAB) are presented. Several examples
are considered for purposes of the comparison of
robustness bounds estimates. Examples are demonstrated to
show the superiority of the robustness bounds estimated by
the proposed method over those obtained by small gain
theorem. In a number of cases, the estimated robustness
bounds are proven to be the exact robustness bounds. / Graduation date: 1993
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/35780 |
| Date | 29 May 1992 |
| Creators | Ahmadkhanlou, Fariborz |
| Contributors | Olas, Andrzej |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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