88
Views
1
CrossRef citations to date
0
Altmetric
Articles

On the existence of the stabilizing solution of generalized Riccati equations arising in zero-sum stochastic difference games: the time-varying case

ORCID Icon &
Pages 913-951 | Received 20 Feb 2020, Accepted 04 May 2020, Published online: 11 Aug 2020

References

  • S. Aberkane, Bounded real lemma for nonhomogeneous Markovian jump linear systems, IEEE. Trans. Automat. Contr. 58(3) (2013), pp. 797–801. doi: 10.1109/TAC.2012.2215532
  • S. Aberkane and V. Dragan, H∞ filtering of periodic Markovian jump systems: Application to filtering with communication constraints, Automatica 48(12) (2012), pp. 3151–3156. doi: 10.1016/j.automatica.2012.08.040
  • S. Aberkane and V. Dragan, Robust stability and robust stabilization of a class of discrete-time time-varying linear stochastic systems, SIAM J. Control Optim. 34(8) (2015), pp. 831–847.
  • S. Aberkane and V. Dragan, On the existence of the stabilizing solution of a class of periodic stochastic Riccati equations, IEEE. Trans. Automat. Contr.65(3) (2020), pp. 1288–1294. doi: 10.1109/TAC.2019.2927589
  • H. Abou-Kandil, G. Freiling, V. Ionescu and G. Jank, Matrix Riccati Equations in Control Systems Theory, Birhauser, Basel, 2003.
  • T. Damm, Rational Matrix Equations in Stochastic Control, Lecture notes in control and information sciences, Springer, 2002.
  • V. Dragan, Robust stabilization of discrete-time time-varying linear systems with Markovian switching and nonlinear parametric uncertainties, Int. J. Syst. Sci. 45(7) (2014), pp. 1508–1517. doi: 10.1080/00207721.2013.860643
  • V. Dragan and T. Morozan, Robust stability and robust stabilization of discrete- time linear stochastic systems, Ann. Acad. Romanian Sci. Ser. Math. Appl. 2(2) (2010), pp. 141–170.
  • V. Dragan, T. Morozan and A.M. Stoica, Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems, Springer, New York, 2010.
  • V. Dragan, S. Aberkane, T. Morozan, On the bounded and stabilizing solution of a generalized Riccati differential equation arising in connection with a zero-sum linear quadratic stochastic differential game. Optim. Contr. Appl. Met. 41(2) (2020), pp. 640–667.
  • G. Freiling and A. Hochhaus, Properties of the solutions of rational matrix difference equations, Adv. Differ. Equ. IV, Comput. Math. Appl. 45 (2003), pp. 1137–1154.
  • A. Halanay, V. Ionescu, Time-varying Discrete Linear Systems, Birkhuser, Basel, 1994.
  • H.J. Maa, W. Zhang and T. Hou, Infinite horizon H2/H∞ control for discrete-time time-varying Markov jump systems with multiplicative noise, Automatica 48(7) (2012), pp. 1447–1454. doi: 10.1016/j.automatica.2012.05.006
  • M. McAsey and L. Mou, Generalized Riccati equations arising in stochastic games, Linear Algebra Appl. 416 (2006), pp. 710–723. doi: 10.1016/j.laa.2005.12.011
  • T. Morozan, Parametrized Riccati equations for controlled linear discrete-time systems with Markov perturbations, Revue Roumaine de Mathématique Pures et Appliquées 43(7–8) (1998), pp. 761–777.
  • V.M. Ungureanu, V. Dragan and T. Morozan, Global solutions of a class of discrete- time backward nonlinear equations on ordered Banach spaces with applications to Riccati equations of stochastic control, Optim. Control Appl. Methods 34(2) (2013), pp. 164–190. doi: 10.1002/oca.2015
  • Z. Yu, An optimal feedback control-Strategy pair for zero-sum linear-Quadratic stochastic differential game: the Riccati equation approach, SIAM J. Control Optim. 53(4) (2015), pp. 2141–2167. doi: 10.1137/130947465

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.