Two-Dimensional Techniques for Linear Discrete-Time Systems

  • Dong ShenEmail author
  • Xuefang Li


This chapter presents the two-dimensional (2D) techniques for addressing the tracking problem of linear discrete-time stochastic systems with varying trial lengths. The Kalman filtering technique is applied to derive the recursive learning gain matrix which guarantees the mean square convergence of the input error to zero. As a consequence, the tracking error will converge asymptotically in mean square sense. The learning gain matrix is derived by optimizing the trace of input error covariance matrix. The precise form of the learning gain matrix depends on statistical properties of random trial lengths and it motivates us to further consider an implementable algorithm.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK

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