非齐次Markovian跳变随机奇异系统的镇定

Stabilization of nonhomogeneous markovian jump stochastic singular systems

研究一类非齐次Markovian跳变随机奇异区间二型模糊系统的随机容许及镇定问题。运用有限分段齐次思想来处理时变的转移速率。首先,构造随机Lyapunov函数,采用广义Ito公式及不等式放缩技术,得到系统随机容许的充分条件;其次,在状态反馈模糊控制器的设计过程中,引入由特定矩阵变量构成的线性变换,将非线性矩阵不等式转化为线性矩阵不等式。此方法的实用性最终通过数值仿真得以验证。

This paper considers the problem of admissibility and stabilization for a class of interval type-2 stochastic singular non-homogeneous Markovian jump systems.It uses the finite piecewise homogeneous idea to deal with the time-varying transfer rate.Firstly,we construct the stochastic Lyapunov function,the generalized Ito formula and inequality scaling technology are adopted to obtain the sufficient conditions for the stochastic admissibility of the system.Secondly,in the process of designing the state feedback fuzzy controller,by introducing the linear transformation composed of specific matrix variables,the nonlinear matrix inequalities are transformed into linear matrix inequalities.Finally,a numerical simulation example verifies the effectiveness of the method.