Multivariable Circle Criterion Research Articles

Robust stability analysis and design method for the fuzzy feedback linearization regulator

A robust stability analysis and design method for a fuzzy feedback linearization regulator is presented. The well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model. Uncertainties and disturbance are assumed to be included in the model structure with known bounds. For these structured uncertainties, stability robustness of the closed system is analyzed in both input-output sense and Lyapunov sense. The robust stability conditions are proposed using multivariable circle criterion and the relationship between input-output stability and Lyapunov stability. Also, based on the stability analysis, a systematic design procedure for the fuzzy feedback linearization regulator is provided. The effectiveness of the proposed analysis and design method is illustrated by a simple example.

Search method for the weighting matrix of the weighted multivariable circle criterion

The weighted multivariable circle criterion contains an arbitrary diagonal matrix that is called the ‘weighting matrix’. In this paper, a method of searching for an adequate weighting matrix is proposed. The choice of the weighting matrix determines the sharpness of the stability criterion obtained. The method is based on the relation between an M-matrix and a positive-definite hermitian matrix. The results of examples show that this method is very useful in obtaining sharper stability conditions.

Input-output stability of composite feedback systems

A new criterion for input-output stability of multiloop systems is presented. The setting proposed by Zames is employed and emphasis is placed upon the multiloop structure of the system. The criterion is derived from the result by Zames and includes, as a special case, some of the previous results about interconnected systems reported by Tokumaru et al., Porter and Michel, and Cook. The criterion is especially useful when applied to multiinput-multioutput feedback systems which have a time-invariant linear system in the forward path and a time-varying nonlinear diagonal gain in the feedback path. It is simpler than, and in certain cases sharper than, the standard multivariable circle criterion.