Robust control design for uncertain nonlinear systems under feedback linearization

A study is made of the design of robust stabilizing controllers for uncertain nonlinear systems which are feedback-equivalent to controllable linear systems. Uncertainty is considered to be parametric and is caused by unknown or time-varying modeled parameters. Uncertainties due to unmodeled dynamics are not addressed. The proposed design method does not necessarily require structure matching conditions between the real plant and the nominal model of the plant. The problem reduces to the design of linear controllers for a linear system perturbed by uncertainties which lie in the range of the control input operator only when the matching conditions are satisfied. The design approach is based on the second method of Lyapunov, wherealgebraic Riccati equations need to be solved