Local L2L2 gain of bifurcation stabilization

Local L2L2 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 L2L2 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 L2L2 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 L2L2 gain. As an example, application to an axial flow compressor control is discussed in detail.