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Global quadratic stabilization of a class of nonlinear systems

✍ Scribed by Sing Kiong Nguang; Minyue Fu

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
138 KB
Volume
8
Category
Article
ISSN
1049-8923

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✦ Synopsis

The problem of quadratic stabilization for a class of nonlinear systems is examined in this paper. By employing a well-known Riccati approach, we develop a technique for designing a state feedback control law which quadratically stabilizes the system for all admissible uncertainties. This state feedback control law consists of linear and nonlinear feedback control terms. The linear feedback control term is generalized from a well-known H result, while the nonlinear term can be viewed as a correcting term for the presence of nonlinear bounded uncertainty. This stabilization result is extended to static output feedback and to systems for which the nonlinear uncertainty satisfies generalized matching conditions. Furthermore, we point out that in the presence of nonlinear uncertainty the global quadratic stability may be destroyed by some arbitrary small mismatched uncertainty in the matrix, and proceed to establish the region of semi-global quadratic stability of the controlled system.

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