Stabilisation and improvement of performance by extension of universal formula in the presence of disturbance
Dept. of Electr. & Comput. Eng., Tehran Univ., IranIEE Proceedings - Control Theory and Applications (Impact Factor: 2.11). 04/2005; 152(2):229 - 237. DOI: 10.1049/ip-cta:20041128
Source: IEEE Xplore
Krstic-Sontag's formula proves constructively that the existence of a control Lyapunov function implies asymptotic stabilisability. A similar result can be obtained for systems subject to unknown disturbances by input-to-state stabilising control Lyapunov functions (ISS-CLFs) and the input-to-state analogue of Krstic-Sontag's formula. A generalisation of the ISS version of Krstic-Sontag's formula is provided by completely parameterising all continuous ISS control laws that can be generated from a known ISS-CLF. Given an ISS-CLF, the synthesis problem reduces to that of finding indexes b(x) and υ(x) that lead to desirable performance, i.e. convergence rate and performance index. A large family of ISS controls is shown that solve the inverse optimal gain assignment problem.
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ABSTRACT: The nonlinear flutter suppression of a typical wing section is investigated. A structural nonlinearity is considered in the pitch direction. Integral-input-to-state stability (iISS) concept is utilised for the construction of a feedback controller. One of the advantages of this design is its simplicity and straightforwardness. A backstepping method is used to compare the results for the typical section, which is a multi-input system. The iISS controller has an outstanding performance in comparison to the backstepping method, especially with regards to the disturbance attenuation problem. A Lyapunov-based controller was also introduced for the system.IET Control Theory and Applications 12/2007; 1(6-1):1638 - 1649. DOI:10.1049/iet-cta:20060455 · 2.05 Impact Factor
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