The stabilization of nonlinear systems with the controller based on approximate polynomial parameter-varying models

This paper investigates the stabilization problem of nonlinear parameter-varying systems, whose controllers are designed based on their approximate polynomial parameter-varying models. First, based on a parameter-dependent polynomial Lyapunov function, a state feedback parameter-dependent controller is proposed, which is also related to the derivatives of parameters to ensure that the approximate polynomial parameter-varying systems are asymptotically stable with specified H_∞ performance under some conditions. Then, it is proved that the designed controller can also locally stabilize the original controlled system. The stabilizable conditions are given in terms of state-and-parameter-dependent linear matrix inequalities, which can be transformed and solved through sum-of-squares theory. Finally, the feasibility and effectiveness of the main results are verified by two numerical examples and an application example.