Indefinite stochastic linear quadratic control with Markovian jumps in infinite time horizon

Xun Li, Xun Yu Zhou, Mustapha Ait Rami

Research output: Journal article publicationJournal articleAcademic researchpeer-review

82 Citations (Scopus)


This paper studies a stochastic linear quadratic (LQ) control problem in the infinite time horizon with Markovian jumps in parameter values. In contrast to the deterministic case, the cost weighting matrices of the state and control are allowed to be indinifite here. When the generator matrix of the jump process - which is assumed to be a Markov chain - is known and time-invariant, the well-posedness of the indefinite stochastic LQ problem is shown to be equivalent to the solvability of a system of coupled generalized algebraic Riccati equations (CGAREs) that involves equality and inequality constraints. To analyze the CGAREs, linear matrix inequalities (LMIs) are utilized, and the equivalence between the feasibility of the LMIs and the solvability of the CGAREs is established. Finally, an LMI-based algorithm is devised to slove the CGAREs via a semidefinite programming, and numerical results are presented to illustrate the proposed algorithm.
Original languageEnglish
Pages (from-to)149-175
Number of pages27
JournalJournal of Global Optimization
Issue number2-3
Publication statusPublished - 1 Nov 2003
Externally publishedYes


  • Coupled generalized algebraic Riccati equations
  • Linear matrix inequality
  • Mean-square stability
  • Semidefinite programming
  • Stochastic LQ control

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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