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Approximate model matching for nonlinear systems

An approximate model matching problem is presented in which the objective is to achieve, via dynamic state feedback, a nonlinear closed-loop system possessing a family of linearizations about constant operating points that matches a prescribed family of linear models from a transfer function viewpoint. A necessary and sufficient solvability condition is derived and an algebraic feedback law construction is provided using an extension of Silverman's structure algorithm to the case of parametrized families of linear systems.