Abstarct: Fuzzy sets theory and systems was developed and extensively applied in previous decades and relevant methods were developed and applied with more or less success depending on the specific problem, and recently, fuzzy control has been successfully applied to a variety of industrial processes. Certainly, without carrying out an in-depth analysis, the design of the system and controller may come with no guarantee of system stability. So, performance and stability are important aspects of designing of such systems. baxsed on these remarks, researches, application of fuzzy systems and this fact that any nonlinear systems can be modeled by a fuzzy system, fuzzy model can be a reasonable model of nonlinear systems in huge number of modeling problems. Among of theses models, Takagi-Sugeno-Kang (T-S) system is mentioned which was presented as new fuzzy system after advent of Mamdani model. Because of linear state form of consequents in the rules of this system and applicable of many linear control theory, this model (T-S) was prospered at rate of high. Thereafter, Parallel Distributed Compensation (PDC) technique was presented as new method for designing and controlling for such type of fuzzy systems. Arrival of theses type of fuzzy models required new methods for stability analysis and controlling subsequently. Extended and innovative methods and relevant conditions for stability analysis of continuous and discrete fuzzy systems were found. In this evolution, most of results require the existence of a common quadratic Lyapunov function. For instance Tanaka and Sugeno proposed a design and stability method for fuzzy systems via Lyapunov direct method. A common positive-definite symmetric matrix