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奇异摄动理论已广泛应用于数学领域以及控制领域,本文研究的基于不完整测量信息的奇异摄动系统的分析和设计问题具有广泛的应用背景和重要的学术价值。针对不能进行慢、快子系统分解的奇异摄动系统,利用广义系统方法,尝试结合线性矩阵不等式处理方法,并运用MATLAB研究基于不完整测量信息的状态估计器设计问题。研究内容分为以下几个方面:1、研究了利用估计值代替丢失的数据实现系统控制,这是研究基于不完整测量信息的控制系统设计的常规手段之一。2、考虑了采样周期长、多速率采样和采样延迟等造成的信息丢失以及传输过程的不可靠性和随机干扰因素造成的信息丢失,借鉴正常系统状态估计问题的研究思路,利用奇异摄动技术和广义系统方法,研究基于不完整测量信息的奇异摄动系统的状态估计方法。3、该研究将为下一步研究基于状态估计器的奇异摄动饱和系统的设计奠定基础,同时为奇异摄动系统理论研究开拓一个新的方向。
The singular perturbation theory has been widely used in the field of mathematics and control. The analysis and design of singularly perturbed systems based on incomplete measurement information in this paper have a wide range of applications and important academic values. Aiming at the singularly perturbed system that can not be used to decompose slow and fast sub-systems, the method of linear matrix inequality (LMI) is studied by using the method of generalized system. And the problem of state estimator design based on incomplete measurement information is studied by MATLAB. The research contents are divided into the following aspects: 1. It is studied that the system control is realized by using the estimated data instead of the missing data. This is one of the conventional methods to study the control system design based on incomplete measurement information. Considering the loss of information caused by long sampling period, multi-rate sampling and sampling delay, as well as the unreliability of the transmission process and the information loss caused by stochastic disturbances, the research idea of the state estimation of normal system is considered. By using the singular perturbation technique And the generalized system method, the state estimation method of singularly perturbed systems based on incomplete measurement information is studied. The research will lay the foundation for further research on the design of singularly perturbed saturated systems based on state estimator, and at the same time open up a new direction for the theoretical study of singular perturbation systems.