Abstract
The recursive-interlacing design procedure is presented in which design objectives of recursive and interlacing steps are explicitly defined. By following the procedure, the designer is guided to choose controls and Lyapunov functions. As the final result, the designer will have either a stabilizing robust control with stability proof completed or, if no control can be generated, certain measure about instabilizability of the system under consideration. It is new and important that the procedure does not impose any a priori structural assumption in the study of robust stabilizability and control design.
The recursive interlacing design is developed based on backward recursion and also contains feedforward interlacing steps which are for compensating EMUs and for properly choosing Lyapunov functions. Other new ideas contained in the procedure include admissible fictitious control, Lyapunov functional, and decomposition of dynamics that do not satisfy existing structural conditions. Hence, the proposed design procedure naturally includes the existing ones as special cases. Despite its widest applicability, the procedure remains to be intuitive. Two third-order vector systems are shown to be robustly stabilizable. Future research should be directed to reveal the full potential of the procedure by searching for more classes of stabilizable uncertain systems and by concluding in a nonlinear setting the necessity of a successful application of the procedure on stabilizability.
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© 1996 Springer-Verlag London Limited
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Qu, Z., Kaloust, J. (1996). A generic Lyapunov procedure to design robust control for nonlinear uncertain systems: Introducing interlacing into recursive design. In: Garofalo, F., Glielmo, L. (eds) Robust Control via Variable Structure and Lyapunov Techniques. Lecture Notes in Control and Information Sciences, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027560
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DOI: https://doi.org/10.1007/BFb0027560
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