Local gain of bifurcation stabilization

Local L 2 gain analysis of a class of stabilizing controllers for nonlinear systems with both stationary and Hopf bifurcations is studied. In particular, a family of Lyapunov functions is first constructed for the corresponding critical system, and simplified sufficient conditions to compute the L 2 gain are derived by solving the Hamilton–Jacobi–Bellman (HJB) inequalities. Local robust analysis for a class of bifurcation stabilizing controllers can then be conducted through computing the local L 2 gain achieved by these controllers at the critical situation. The results obtained in this paper provide useful guidance for selecting a robust controller from a given class of stabilizing controllers in terms of L 2 gain. As an example, application to an axial flow compressor control is discussed in detail.