Linear-Quadratic Control Problems

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


In this chapter, we study the main algebraic equations of the linear steady state control theory: the Lyapunov and Riccati algebraic equations, for both singularly perturbed and weakly coupled systems. We derive the corresponding recursive, reduced-order parallel algorithms for the solution of these equations in the most general case when the problem matrices are functions of a small perturbation parameter. The numerical decomposition has been achieved, so that only low-order systems are involved in algebraic computations. The introduced recursive methods are of the fixed point type and can be implemented as synchronous parallel algorithms (Bertsekas and Tsitsiklis, 1989; 1991).


Assure Eter BoRal 


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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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