{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:18:05Z","timestamp":1760242685440,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,3,14]],"date-time":"2016-03-14T00:00:00Z","timestamp":1457913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper addresses the problem of solving discrete-time                                        H               \u221e                                  control problems for periodic systems. The approach for solving such a type of equations is well known in the literature. However, the focus of our research is set on the numerical computation of the stabilizing solution. In particular, two effective methods for practical realization of the known iterative processes are described. Furthermore, a new iterative approach is investigated and applied. On the basis of numerical experiments, we compare the presented methods. A major conclusion is that the new iterative approach is faster than rest of the methods and it uses less RAM memory than other methods.<\/jats:p>","DOI":"10.3390\/a9010020","type":"journal-article","created":{"date-parts":[[2016,3,14]],"date-time":"2016-03-14T11:03:45Z","timestamp":1457953425000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Iterative Solution to Discrete-Time H\u221e Control Problems for Periodic Systems"],"prefix":"10.3390","volume":"9","author":[{"given":"Ivan","family":"Ivanov","sequence":"first","affiliation":[{"name":"Faculty of Economics and Business Administration, Sofia University \u201cSt. Kliment Ohridski\u201d, 125 Tsarigradsko Shosse Blvd., bl.3, 1113 Sofia, Bulgaria"}]},{"given":"Boryana","family":"Bogdanova","sequence":"additional","affiliation":[{"name":"Faculty of Economics and Business Administration, Sofia University \u201cSt. Kliment Ohridski\u201d, 125 Tsarigradsko Shosse Blvd., bl.3, 1113 Sofia, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2016,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01211501","article-title":"Differential periodic Riccati equations existence and uniqueness of nonnegative definite solutions","volume":"6","author":"Pastor","year":"1993","journal-title":"Math. Control Signal Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Abou-Kandil, H., Freiling, G., Ionescu, V., and Jank, G. (2003). Matrix Riccati Equations in Control Systems Theory, Birhauser.","DOI":"10.1007\/978-3-0348-8081-7"},{"key":"ref_3","unstructured":"Bittanti, S., and Colaneri, P. (2009). Periodic Systems, Filtering and Control, Springer-Verlag."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Halanay, A., and Rasvan, V.l. (2000). Stability and Stable Oscillations in Discrete Time Systems, Gordon and Breach.","DOI":"10.1201\/9781482283280"},{"key":"ref_5","unstructured":"Varga, A. (2005, January 12\u201315). On solving periodic differential matrix equations with applications to periodic system norms computation. Proceedings of the 44th IEEE Conference on Decision and Control, CDC-ECC \u201905, Seville, Spain."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1002\/nla.604","article-title":"On solving periodic Riccati equations","volume":"15","author":"Varga","year":"2008","journal-title":"Numer. Linear Algebra Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1002\/rnc.3131","article-title":"On computing the stabilizing solution of a class of discrete-time periodic Riccati equations","volume":"25","author":"Dragan","year":"2015","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_8","unstructured":"Dragan, V., Aberkane, S., and Ivanov, I.G. (2014, January 7\u201311). An iterative procedure for computing the stabilizing solution of discrete-time periodic Riccati equations with an indefinite sign. Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems, MTNS 2014, Groningen, The Netherlands."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1080\/00207179.2011.578261","article-title":"A numerical procedure to compute the stabilizing solution of game theoretic Riccati equations of stochastic control","volume":"84","author":"Dragan","year":"2011","journal-title":"Int. J. Control"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s11075-010-9432-7","article-title":"Computation of the stabilizing solution of game theoretic Ric-cati equation arising in stochastic H\u221e control problems","volume":"57","author":"Dragan","year":"2011","journal-title":"Numer. Algorithms"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.sysconle.2009.11.006","article-title":"An iterative algorithm to solve state-perturbed stochastic algebraic Riccati equations in LQ zero-sum games","volume":"59","author":"Feng","year":"2010","journal-title":"Syst. Control Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1080\/00207170903460493","article-title":"Iterative algorithm to compute the maximal and stabilizing solutions of a general class of discrete-time Riccati-type equations","volume":"83","author":"Dragan","year":"2010","journal-title":"Int. J. Control"},{"key":"ref_13","first-page":"57","article-title":"An Improved Method for Solving a System of Discrete-Time Generalized Riccati Equations","volume":"3","author":"Ivanov","year":"2011","journal-title":"J. Numer. Math. Stoch."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/9\/1\/20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:20:40Z","timestamp":1760210440000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/9\/1\/20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,14]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3]]}},"alternative-id":["a9010020"],"URL":"https:\/\/doi.org\/10.3390\/a9010020","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2016,3,14]]}}}