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针对一类在切换时刻具有脉冲行为的Markov切换非线性随机系统,首先,应用切换的Lyapunov函数方法研究系统的稳定性,给出系统几乎必然稳定的充分条件,该条件不依赖于系统的矩稳定性;然后,进一步对线性系统的稳定化问题进行分析与设计,对随机子系统的控制结构同时出现在方程的位移部分与扩散部分,给出相应的状态反馈增益矩阵的求解方法;最后,数值算例说明了所设计方法的有效性.
For a class of Markov switched nonlinear stochastic systems with impulsive behavior at the switching moment, firstly, the switched Lyapunov function method is used to study the stability of the system. The sufficient and necessary conditions for the system to be almost stable are obtained. The condition does not depend on the moment stability of the system Then, the stability of the linear system is further analyzed and designed. The control structure of the stochastic subsystems appears in the displacement part and the diffusion part of the equation at the same time, and the solution of the state feedback gain matrix is given. Finally, the numerical value The example shows the effectiveness of the proposed method.