Indefinite stochastic LQ control with jumps

Xun Li, Xun Yu Zhou, Mustapha Ait Rami

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


This paper studies a stochastic linear quadratic (LQ) 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 indefinite 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)1693-1698
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Publication statusPublished - 1 Jan 2001
Externally publishedYes


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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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