Controller design for lipschitz nonlinear system using linear matrix inequalities

Abstract

All real practical systems have nonlinear dynamics. To linearize the system and to design a controller for the linearized plant is often inadequate and insufficient for many complex systems. Thus, controller design for nonlinear systems still forms an important part of research. The paper proposes a simple method of stabilizing a class of nonlinear system. The nonlinearity is assumed to be norm bounded and thus the class of system considered is the class of Lipschitz nonlinear system. A state feedback control law is derived in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated with the help of examples.