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Robust SDC parameterization for a class of Extended Linearization systems

We consider nonlinear regulation of systems with parametric uncertainty. Under mild conditions, these systems can be brought into a psuedo-linear form known as extended linearization. Under this formulation, conventional linear control synthesis methods can be applied. One popular technique that mimics the LQR method of optimal linear control is referred to as the State-Dependent Riccati Equation (SDRE) approach. SDRE control relies on a non-unique factorization of the system dynamics known as the State Dependent Coefficient (SDC) parameterization. Under system uncertainty, each SDC parameterization will produce its own radius of stability in a region of interest in the state space. In this paper a method to compute the radius of stability in a special class of systems is used to obtain the SDC parameterization which results in the maximum radius of stability for the original nonlinear system in the region of interest. It is shown that the problem of finding the maximum radius of stability from a hyperplane of SDC parameterizations can be reduced to constrained minimization of the spectral norm of a comparison system.