A Matrix Pencil Formulation for Non-Conservative Realization of Scaling-Based Controllers for Feedforward-Like Systems

We develop a general matrix pencil based approach for efficient non-conservative realization of dual dynamic high-gain scaling based control designs for a class of uncertain feedforward-like nonlinear systems. It is shown that the control design can be cast into a set of matrix pencil based sub-problems capturing the detailed system structure, state dependence structure of uncertain terms, and precise roles of design freedoms in the context of detailed structures of Lyapunov inequalities. The design freedoms in the dynamic high-gain scaling based design are extracted in terms of eigenvalues of the formulated matrix pencil structures. It is seen that the proposed matrix pencil based approach greatly reduces design conservatism and algebraic complexity compared to prior results on dynamic high-gain scaling based control designs.