Linear Stochastic Systems

  • Zoran Gajić
  • Xuemin Shen
Part of the Communications and Control Engineering Series book series (CCE)


In this chapter, we study the stochastic optimal control of linear time invariant singularly perturbed and weakly coupled systems in both continuous and discrete-time domains. The main issue in the linear optimal stochastic control is the design of the optimal Kalman filter which has the same order as a dynamical system under consideration. In the case of large scale systems composed of slow, fast, and weakly coupled state variables, it is possible to replace the design of the global Kalman filters in terms of the reduced-order Kalman filters. In addition to these on-line simplifications, we also present the simplified calculations of the regulator and filter gains by using the corresponding parallel algorithms derived in Chapters 2 and 3.


Kalman Filter Algebraic Riccati Equation Local Filter Linear Stochastic System Couple State Variable 
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Copyright information

© Springer-Verlag London Limited 1993

Authors and Affiliations

  • Zoran Gajić
    • 1
  • Xuemin Shen
    • 2
  1. 1.Department of Electrical and Computer EngineeringRutgers UniversityUSA
  2. 2.Department of Electrical EngineeringUniversity of AlbertaEdmontonCanada

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