Stability analysis and robust stabilization of a class of nonlinear systems based on stability radii

The concept of Stability Radii, first proposed by Charles Van Loan [1], is a measure of robust stability for linear systems. In this paper, the exponential stability and robust stabilization of a class of nonlinear systems will be discussed. The class of nonlinear systems under consideration are the ones that can be separated into a nominal linear part plus a nonlinear perturbation with the linear part in Metzlerian form. It has been shown that if the norm of the nonlinear perturbations is bounded by the complex stability radius of the nominal system, then the entire system is stable. Here, we will apply an output feedback gain to the linear part of the system to increase its stability radius to be equal or greater than a given desired value.