Robust Feedback Design of Cascaded Nonlinear Systems with Structural Uncertainty

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This paper is concerned with the robust stabilization and robust L2 disturbance attenuation of a class of cascaded nonlinear systems with structural uncertainties. The design tools are construction of a Lyapunov function for robust stabilization and a storage function for robust L2 gain performance. The cascaded system consists of two subsystems called the x-subsystem and the ξ-subsystem. It is shown that if for each subsystem there exist Lyapunov functions satisfying Hamilton-Jacobi inequalities related with nominal subsystems, then a robust stabilizing controller can be constructed such that the sum of the functions becomes a Lyapunov function for the cascaded system with uncertainties. This concept is extended to the construction of the storage function and the controller for the robust L2 disturbance attenuation problem by introducing an appropriate weight into the sum of the subsystem's Lyapunov functions. It is also shown that these results can be extended to solve robust design problems for the ξ-subsystem with a triangular structure.

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