T-S离散模糊系统的二次稳定性

Quadratic Stability of T-S Discrete Fuzzy Systems

研究了T-S离散模糊系统的二次稳定性,目的是得到更简单的稳定性条件·首先,引入适合于T-S离散模糊系统的Lyapunov函数,得到了该系统稳定的充分条件·然后利用Schur补将非线性矩阵不等式问题转换成线性矩阵不等式问题,从而把被研究系统转化为凸组合系统,提出了基于LMI的更为简单的二次稳定性的充分条件·最后,给出了一个计算例子,计算结果说明可以使用LMI和MATLAB求解这类问题,同时证明了上述方法的优越性·利用该方法可以进一步研究T-S离散模糊系统的鲁棒控制、H∞控制等问题·

Studies the quadratic stability of T-S discrete fuzzy systems for the purpose to obtain the simpler conditions for stability than that as shown in earlier works. The sufficient conditions for quadratic stability are given by introducing the Lyapunov function adaptable to T-S discrete fuzzy systems. Then, the nonlinear matrix inequalities were converted into linear matrix inequalities （LMIs） by using the Schur complement, thus converting the T-S discrete fuzzy systems into convex combination ones with simpler LMI-based sufficient conditions given to quadratic stability. A numerical simulation was done to exemplify that such problems can be solved by using LMI and MATLAB and verify that the result of the theorem derived in this paper is better than those in earlier works. In this way the problems of robust control and H∞ control could be studied further.