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).


Parallel Algorithm Riccati Equation Lyapunov Equation Algebraic Riccati Equation Fast Subsystem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations