On the domain of attraction and local stabilization of nonlinear parameter-varying systems

In this paper, the domain of attraction (DA) and the local stabilization problem are investigated under the nonlinear parameter-varying (NPV) framework. Specifically, to take into account the time-varying parameter, we generalize the definition of robust DA (RDA) and propose the concept of parameter-dependent DA (PDA) for NPV systems, together with the sum-of-squares (SOS) conditions for their estimations. Differently from the existing DA-related works, the theoretical results in this paper can be applied to a large class of nonlinear polynomial systems including the time-invariant, the parameter-dependent, and the uncertain ones. Moreover, the commonly used iterative/coordinate-wise search is avoided because we eliminate the bilinear product terms between the Lyapunov functional and the SOS multipliers. We also consider the local stabilization problem of NPV systems, in which the RDA can be specified as a control performance index. Finally, several examples are given for illustration purposes.