Piecewise Quadratic Stability Analysis for Local Model Networks

This paper deals with the problem of stability analysis of dynamic local model networks. Established methods in this context are mainly based on Lyapunov stability theory and are targeted to be as little conservative as possible. In previous works the so called Piecewise Quadratic Lyapunov approach was developed. For discrete time systems the state space is partitioned into local subspaces, which are defined by the validity functions of the local models. Because of the overlapping validity functions, so-called uncertainty terms exist which describe the influence of the dynamics of other local models. In this respect, it is necessary to pay attention to the determination of these uncertainty terms. This paper presents and discusses a method to determine the upper bounds for the uncertainty terms of the local models. The method is based on quadratic optimization to achieve a stability criterion where the conservatism is not additionally increased. The effectiveness of the proposed method is shown by a simulation example in connection with the Piecewise Quadratic Lyapunov approach as a stability criterion.