Nonlinear Hinfinity-control of nonsmooth time-varying systems with application to friction mechanical manipulators

Nonlinear H"~-controller synthesis is developed for nonsmooth time-varying systems via measurement feedback. A local H"~-controller is derived by means of a certain perturbation of the differential Riccati equations, appearing in solving the H"~-control problem for the linearized system, when these unperturbed equations have bounded positive semidefinite solutions. Stabilizability and detectability properties of the control system are thus ensured by the existence of the proper solutions of the unperturbed differential Riccati equations, and hence the proposed synthesis procedure obviates an extra (formidable in the nonlinear case) work on verification of these properties. Theoretical results are applied to a position tracking control problem and, particularly, a regulation problem for mechanical systems with friction. Performance issues of the nonlinear H"~-tracking controller are illustrated in a simulation study made for a two degrees-of-freedom robot manipulator.

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