Piecewise Fuzzy Model Construction and Controller Design based on Piecewise Lyapunov Function

This paper presents piecewise fuzzy model construction divided by arbitrary affine hyper-planes and controller design based on the so-called piecewise Lyapunov function. In our previous papers, we proposed the switching fuzzy model construction method with arbitrary dividing hyper- planes. However, we assumed that the dividing planes contain the origin, that is, linear hyper-planes in the papers. In this paper, we propose piecewise fuzzy model construction method with arbitrary dividing hyper-planes which are permitted not to pass through the origin. We can obtain sectors which can cover nonlinear dynamics more tightly than ordinary method. By utilizing continuity matrices which are constructed from coefficients of dividing hyper-planes, we construct piecewise fuzzy model which is continuous on boundaries of divided regions caused by dividing planes. Moreover, we derive controller design conditions based on the so-called piecewise Lyapunov function in terms of LMIs.