A generalized sector-bound approach to feedback stabilization of nonlinear control systems

This paper proposes and develops a generalized sector-bound approach to feedback stabilization of nonlinear control systems described by state-space models. This approach is inherited from the methodology of the sector-bounded or passive nonlinearities and influenced by the concept of absolute and quadratic stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. More importantly, it has a close connection to gain scheduling and switching control. A path of equilibria is programmed on the basis of the assumption of centered- epsilon-cover, which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically. Simulation results are worked out to illustrate our proposed design method. Copyright (c) 2012 John Wiley & Sons, Ltd.