Algebraic riccati equations and spectral factorizations

Mi-Ching Tsai, Da Wei Gu

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In the last chapter, it was discussed that the algebraic Riccati equation (ARE) need be solved in order to obtain the state-space solutions of the normalized coprime factorizations. In Chap. 2, the Lyapunov equation was employed to determine the controllability and observability gramians of a system. Both the algebraic Riccati and Lyapunov equations play prominent roles in the synthesis of robust and optimal control as well as in the stability analysis of control systems. In fact, the Lyapunov equation is a special case of the ARE. The ARE indeed has wide applications in control system analysis and synthesis. For example, the state-space formulation for particular coprime factorizations with a J-lossless (or dual J-lossless) numerator requires solving an ARE; in turn, the J-lossless and dual J-lossless systems are essential in the synthesis of robust controllers using the CSD approach. In this chapter, the ARE will be formally introduced. Solution procedures to AREs and their various properties will be discussed. Towards the end of this chapter, the coprime factorization approach to solve several spectral factorization problems is to be considered.

Original languageEnglish
Title of host publicationAdvances in Industrial Control
PublisherSpringer International Publishing
Pages171-209
Number of pages39
Edition9781447162568
DOIs
Publication statusPublished - 2014 Jan 1

Publication series

NameAdvances in Industrial Control
Number9781447162568
ISSN (Print)1430-9491
ISSN (Electronic)2193-1577

Fingerprint

Riccati equations
Factorization
Control system synthesis
Control system analysis
Observability
Controllability
Control systems
Controllers

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Industrial and Manufacturing Engineering

Cite this

Tsai, M-C., & Gu, D. W. (2014). Algebraic riccati equations and spectral factorizations. In Advances in Industrial Control (9781447162568 ed., pp. 171-209). (Advances in Industrial Control; No. 9781447162568). Springer International Publishing. https://doi.org/10.1007/978-1-4471-6257-5_7
Tsai, Mi-Ching ; Gu, Da Wei. / Algebraic riccati equations and spectral factorizations. Advances in Industrial Control. 9781447162568. ed. Springer International Publishing, 2014. pp. 171-209 (Advances in Industrial Control; 9781447162568).
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Tsai, M-C & Gu, DW 2014, Algebraic riccati equations and spectral factorizations. in Advances in Industrial Control. 9781447162568 edn, Advances in Industrial Control, no. 9781447162568, Springer International Publishing, pp. 171-209. https://doi.org/10.1007/978-1-4471-6257-5_7

Algebraic riccati equations and spectral factorizations. / Tsai, Mi-Ching; Gu, Da Wei.

Advances in Industrial Control. 9781447162568. ed. Springer International Publishing, 2014. p. 171-209 (Advances in Industrial Control; No. 9781447162568).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Tsai M-C, Gu DW. Algebraic riccati equations and spectral factorizations. In Advances in Industrial Control. 9781447162568 ed. Springer International Publishing. 2014. p. 171-209. (Advances in Industrial Control; 9781447162568). https://doi.org/10.1007/978-1-4471-6257-5_7