离散时间二型模糊线性时滞系统的可达集估计

Reachable set estimation of discrete-time type-2 fuzzy linear systems with time delays

研究了一类带有时滞和外部输入扰动的复杂非线性系统的可达集估计问题。考虑系统的隶属度函数具有不确定性,利用区间二型模糊模型对非线性系统建模,通过有效的分析与设计方法,研究离散时间二型模糊线性时滞系统的可达集分析与估计问题,寻求在任意初始条件下使所有系统状态收敛的可达集。首先,设计全新的Lyapunov-krasovskii泛函,在证明过程中结合区间二型模糊集性质;然后,利用新的矩阵不等式界定交叉项,从而得到了保守性较小的离散时间区间二型模糊时滞系统的可达集界定充分条件,定理条件可以保证系统的所有状态都收敛在一个椭圆内,而且定理的条件可由一系列线性矩阵不等式表示并用MATLAB软件实现;最后,通过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 problem of reachable set estimation is studied for a class of nonlinear system with both time delays and external disturbance.Considering the uncertainties in the membership functions,the nonlinear system can be modeled by the discrete-time type-2 fuzzy linear systems.By utilizing effective analysis and synthesis methods,this paper firstly investigates the reachable set estimation problem of discrete-time type-2 fuzzy time-delay systems that all states of the system are converged into reachable set under every initial conditions.By constructing a set of appropriate Lyapunov Krasovskii functionals,combining the properties of type-2 fuzzy sets in the proof process,and by using the new matrix inequalities to bound the crossing terms,a sufficient condition is obtained to ensure all the states to be bounded in an ellipsoid.The condition of the theorem is characterized by the solution of linear matrix inequalities.The feasibility of this result is verified by a numerical simulation example.