Fuzzy-rule-based model reduction for switched nonlinear systems

The reduced-order model approximation problem is investigated for discrete-time nonlinear switched systems in T-S fuzzy framework in this paper. For a high-dimensional hybrid nonlinear system, our aim is focused on the construction of a reduced-dimensional hybrid model, which not only approximates the original system well with a pre-specified system performance level but also translates it into a lower-dimensional multi-mode system. Based on the average dwell time technique and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the mean-square exponential stability with a weighted ℋ
_∞
system performance level for the augmented error system. The model approximation problem with pre-specified performance is solved by using the projection technique, which casts the reduced-order hybrid model into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm.