随机2D离散系统的统计特性

The Statistical Properties of Stochastic 2-D Discrete-time Systems

随机系统在研究方法上不同于确定性系统。目前 ,对存在随机干扰的 2 -D状态空间模型的研究较为少见。该文针对 2 -D随机多输入多输出线性时变系统的状态变量表达式 ,讨论了系统状态的统计特性 ,给出了系统的状态均值、方差和协方差阵的计算公式 ,并举例说明了该计算法。这些结果对进一步展开对随机 2-D系统的状态估计 ,最优控制和其它方面的研究都具有重要意义。

The analysis and design methods in stochastic systems are different from those in deterministic systems.By now only few results on the 2-D state space model with stochastic input were reported in the literature.This paper studied the statistical properties of the state for the 2-D multi input multi output linear time variant systems with stochastic input ,the state expectation,variance and covariance matrices for the systems under consideration are given,as well as an example to explain the method.The results obtained in this paper are very important for the further studies on the state estimation and optimal control of 2-D linear systems with stochastic input.