离散时间T-S模糊奇异时滞系统的广义耗散控制

Extended dissipative control for discrete-time T-S fuzzy singular systems with time-delays

针对一类带有时变时滞和外部干扰的复杂非线性奇异系统,利用离散时间T-S模糊模型对其建模。基于李雅普诺夫稳定性理论,研究了离散时间T-S模糊奇异时滞系统的广义耗散容许性问题。首先,通过设计新的李雅普诺夫泛函,在证明过程中考虑以往常被忽略的时滞项交叉项,并利用改进的互凸组合方法和最新的矩阵不等式,引进不依赖于系统状态和李雅普诺夫函数矩阵的自由权值矩阵变量来界定三重、二重差分求和项,从而得到了保守性较小的离散时间T-S模糊奇异时滞系统的广义耗散容许性充分条件;其次,由于奇异系统的特殊性,为了确保定理的条件能用MATLAB软件实现,定理的条件可转化为平方和形式;最后,通过数值仿真算例验证了本文所得结论和方法的正确性和有效性。

In this paper,the problem of extended dissipativity analysis for complex nonlinear singular systems with time-varying delays and bounded input disturbances is studied.The nonlinear singular system is modeled by T-S fuzzy singular system.Firstly,based on new Lyapunov-Krasovskii functional,in which the cross terms of time delays are considered,and by using an improved reciprocally convex combination approach and some new techniques on matrix convexification to bound the forward difference of the double and the triple summation terms in the Lyapunov function.A novel extended dissipativity based admissibility criterion of T-S fuzzy singular systems is obtained.Secondly,due to the special structure of the singular system,the derived condition can be expressed in terms of sam-of-squares(SOS).Finally,a numerical example is provided to demonstrate the effectiveness of this proposed approach.