Robustness of linear and nonlinear H∞ controllers in unified framework

This paper shows that not only the central controllers but all linear H_∞ state feedback, output feedback, static output feedback controllers of the most general nominal continuous linear plant are robust despite perturbations. Moreover, with some additional mild assumptions, any (linear or nonlinear) H_∞ controller has such robustness as well. Such results hold true even for a very general class of hybrid systems, which includes the discrete time system, sampled-data system, etc. As a special case. Such results are extended to a general class of nonlinear systems. In contrast to previous papers which combined Riccati/Hamilton-Jacobi-Isaacs equations with implicit function theorem and the completing square technique to obtain the desired robustness, the new approach presented here uses only the most common gain and internally stabilizing conditions of any H_∞ controllers that yields the desired results with no extra conditions involved