Feedback Design Methods for Nonlinear Systems

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This research involves the development of a feedback design methodology for nonlinear systems, based on a nonlinear enhancement of classical root-locus theory. This proposed nonlinear "frequency domain" methodology, for example, is capable of designing, in a systematic way, stabilizing "lead-lag" compensators, nonlinear PD controllers for set-point control, feedback strategies for disturbance decoupling with closed-loop stability or perhaps even asymptotic tracking and disturbance rejection for a broad class of nonlinear systems, based on nonlinear analogues of classical control concepts such as relative degree or nonlinear "minimum phase" properties. This methodology has been successfully employed for stabilization in the large of scalar, affine (in the control) "minimum phase" nonlinear systems under certain regularity conditions. However, many applications of interest are multivariable, sometimes not affine, and very often have singularities. This work will systematically develop and extend this design methodology so as to include such systems, drawing where necessary on techniques in geometric control, dynamical systems and classical control.