${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems

This paper is concerned with the problem of
${\cal H}_{\infty}$
model reduction for Takagi–Sugeno (T–S) fuzzy stochastic systems. For a given mean-square stable T–S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an
${\cal H}_{\infty}$
performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.