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We present control algorithms for stabilization and asymptotic disturbance rejection for Hammerstein systems with positive real linear dynamics. To do this, we extend the nonlinear controller modification technique of Bernstein and Haddad (1994) to include matched plant disturbances. The controller is based on a Lyapunov function that estimates the disturbance bound. These estimates are then used to construct high-gain switching controllers that guarantee convergence of the plant output while accounting for input nonlinearities.