离散时间二型模糊双线性时滞系统的可达集估计与耗散性

Reachable Set Estimation and Dissipativity of Discrete-Time Type-2 Fuzzy Bilinear Systems with Time-Varying Delays

文章研究了一类带有时变时滞和外部干扰的非线性系统的可达集估计与耗散控制问题.首先,考虑非线性系统的不确定参数,将非线性系统建模为区间二型模糊双线性时滞系统.其次,通过构造Lyapunov-Krasovskii泛函,提出区间二型模糊状态反馈控制准则,并利用反互凸组合引理界定二、三重时滞差分交叉项,得到保守性较小的区间二型模糊双线性闭环系统的可达集估计条件及系统严格耗散稳定性充分性条件.定理的条件可以保证系统的所有状态都收敛在一个椭圆内,并通过序列线性规划矩阵方法得到模糊控制器.最后,给出数值算例和仿真结果验证所得结论的有效性和正确性.

In this paper,the problems of reachable set estimation and dissipative control for a class of nonlinear systems with time-varying delays and output dis-turbance are studied.Firstly,considering the parameter uncertainties in nonlinear system,the nonlinear system is modeled into the interval type-2 fuzzy bilinear delay systems.Secondly,by constructing Lyapunov Krasovskii functional,an interval type-2 fuzzy state-feedback control criterion is proposed,and a sufficient delay-dependent less conservative dissipative stable condition of reachable set estimation is obtained for interval type-2 fuzzy bilinear closed-loop systems via the reciprocally convex combination approach.The derived theorem can guarantee that all the states with initial conditions are bounded in an ellipsoid.The fuzzy controller can be obtained by using sequential linear programming matrix method.Finally,one simulation example is presented to illustrate the correctness of the derived result in the paper.