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针对实际系统中非线性扰动以一定概率存在的情况,讨论广义马氏跳变系统的控制问题.首先,运用Bernoulli变量描述系统中非线性扰动的存在与否,建立相应的数学模型,得到在上述一般条件下系统的随机容许性与解的存在唯一性条件.然后,以LMI形式给出模态依赖和模态独立控制器的存在条件.与现有结果相比,所得结果考虑了非线性扰动的存在概率,具有较小的保守性.最后,通过数值例子验证了所得结果的有效性和优越性.
In this paper, we discuss the control problems of generalized Markov transition systems with respect to the existence of nonlinear perturbations in practical systems.Firstly, we use Bernoulli variables to describe the existence of nonlinear perturbations in the system and establish corresponding mathematical models, Under general conditions, the existence and uniqueness of the stochastic admissibility and the solution of the system are given. Then, the existence conditions of modal dependence and modal independent controller are given in terms of LMI. Compared with the existing results, the obtained results take into account the nonlinear perturbation The existence probability is smaller and the conservativeness is lower.Finally, the numerical results show the effectiveness and superiority of the results obtained.