An approach to analysis and stabilization of Takagi-Sugeno fuzzy control systems via superstability conditions

The linear matrix inequality approach is an efficient way of analyzing stability and solving various fuzzy controller design problems for Takagi-Sugeno (T-S) fuzzy systems, which represent a wide class of nonlinear (including chaotic) systems. This work deals with the possibilities of applying the approach based on another sufficient stability condition – superstability – to the T-S fuzzy control systems. Superstability conditions are formulated in terms of the elements of system matrices of local linear subsystems of the T-S fuzzy model; and their implementation can simplify the study in the situations, when there arise some difficulties with the analysis and control of T-S fuzzy systems via LMI approach. In the work we present a general approach to the output superstabilization of a class of T-S fuzzy systems and investigate the existence conditions of the superstabilizing state feedback fuzzy controller. The advantages of the offered approach are the simplicity of implementation and the possibility to ensure the given characteristics of the transient response. The efficiency of the technique is illustrated by the example of the solution of the chaos suppression problem for the Lorenz system.