| In the last few decades, T-S fuzzy systems have receivedincreasingly attention. The reasons are as follows. First, there is no doubtthat the system is simplicity, generality and easy to grasp. Next, they arevalid for describing the major categories of nonlinear systems by feat ofan averaged sum of linear models. Undoubtedly, stability analysis of T-Sfuzzy systems are very important issues.Lyapunov stability theory is an indispensable tool to solve thestability issues. The simplest approach for T-S fuzzy continuous-timesystems consists in looking for a common quadratic Lyapunov function.However, common quadratic Lyapunov function might not exist for someT-S fuzzy systems. Accordingly, more general classes of Lyapunovfunctions have been developed. Among all the Lyapunov functions, fuzzyLyapunov functions have drawn lots of attention. Fuzzy Lyapunovfunctions can be employed to tackle the stability issues for bothcontinuous-time systems and discrete-time systems.But, since the time derivative of the fuzzy weighting functionsappear in the Lyapunov inequality, a problem when applying the fuzzyLyapunov functions arise. The continuous-time stability conditionscannot be well handled via linear matrix inequalities. Before this, theupper bounds on time derivative of the fuzzy weighting functions wasprovided. Yet in practice the upper bounds are often the same value. Thispaper will discuss the upper bounds under the satisfied condition. Thepurpose of this paper is to find out a method to reduce theconservativeness for T-S fuzzy systems.Then, more work should be madein order to apply this method to second-order time derivative of the fuzzyweighting functions. |
PDF Full Text Request