关于不确定线性连续随机系统的协方差上下界研究*

on Upper and Lower Covariance Bounds for Uncertain Linear Continuous-Time Stochastic Systems

中文关键词  不确定系统  系统分析  线性系统  随机系统

英文关键词  uncertain systems  system synthesis  covariance characteristics

中文摘要

      在随机控制领域中，线性系统的鲁棒性质及性能指标常常以其稳态状态协方差矩阵的形式给出。本文研究在状态矩阵及噪声矩阵中均含有不确定性的线性连续随机系统的稳态状态协方差上下界确定问题，从而为基于协方差性能指标的控制与模型简化提供必要的理论分析基础.

英文摘要

      In the field of stochastic control，many robustness properties and performance requirements of linear systems are given explicitly in terms of the state covariance matrix.In this paper，the problem of determining upper and lower state -covariance bounds is studied for linear continuous-time stochastic systems with uncertainties in both the state matrix and the noise matrix.An effective algebraic Riccati equation approach is exploited to obtain the upper and lower covariance bounds.A numerical example is provided to demonstrate the directness and applicability of the proposed synthesis method.The main results of the present paper offer the basis of theoretical synthesis for the covariance- based control and model reduction.