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Solution of the Riccati equation

  • Tobias Damm
Chapter
Part of the Lecture Notes in Control and Information Science book series (LNCIS, volume 297)

Abstract

In Chapter 2 we have discussed various optimal and worst-case stabilization problems for linear stochastic control systems and reformulated them in terms of rational matrix inequalities. Now we analyze these matrix inequalities and the corresponding matrix equations. To this end, we first introduce an abstract form of the Riccati operators met in the Sections 2.1 – 2.3, and the definite and the indefinite constraints mentioned in Remark 2.3.7. Recall that the LQ-stabilization problem and the Bounded Real Lemma lead to Riccati equations with definite constraints, while the disturbance attenuation problem involves an indefinite constraint.

Keywords

Linear Matrix Inequality Riccati Equation Noise Intensity Newton Iteration Deterministic Case 
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.

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Authors and Affiliations

  • Tobias Damm
    • 1
  1. 1.Technische Universität Braunschweig Institut für Angewandte Mathematik 38023 BraunschweigGermany

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