46b90161-e787-497c-b64a-ec58f5dcc81220210318082720236wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL1991-876310.37394/23203http://wseas.org/wseas/cms.action?id=4073220202022020201510.37394/23203.2020.15http://wseas.org/wseas/cms.action?id=23195Mixed H2/H∞ Control Synthesis for Discrete-time Linear Positive Systems using Enhanced Set of Linear Matrix InequalitiesDušanKrokavecDepartment of Cybernetics and Artificial Intelligence, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Košice, SLOVAKIAAnnaFilasováDepartment of Cybernetics and Artificial Intelligence, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Košice, SLOVAKIAThis paper provides an idea, resulting from linear matrix inequality representation of parameter constraints of discrete-time linear positive systems, to formulate state-feedback synthesis for this class of systems. The design conditions are imposed to obtain control respecting existing strictly positivity or non-negativity in the system matrix description. Formulated as a linear matrix inequality feasibility problem it is reiterated that approach leads iteratively to estimation of norms of closed-loop system71420207142020270281https://www.wseas.org/multimedia/journals/control/2020/a565103-047.pdf10.37394/23203.2020.15.28https://www.wseas.org/multimedia/journals/control/2020/a565103-047.pdf10.3182/20050703-6-cz-1902.00613M. Ait Rami and F. Tadeo, Linear programming approach to impose positiveness in closed-loop and estimated states,Proc. 16th Int. Symp.Mathematical Theory of Networks and Systems,Kyoto, Japan, 2006, pp. 2470–2477.10.1109/acc.2007.4282448M. Ait Rami, F. Tadeo and A. Benzaouia, Control of constrained positive discrete systems,Proc. 2007 American Control Conf. ACC’07,New York, USA, 2007, pp. 5851–5856.10.1155/2014/856356B. Canto, R. Cantó and S. Kostova, Stabilization of positive linear discrete-time systems by using a Brauers theorem,Scientific World Journal, Vol. 2014, 2014, pp. 1–6.G.R. Duan and H.H. Yu,LMIs in Control Systems. Analysis, Design and Applications, CRCPress, Boca Raton, 2013.10.23919/ecc.2018.8550565Y. Ebihara, H2state-feedback synthesis under positivity constraint. Upper and lower bounds computation of the achievable performance, Proc. 16th European Control Conf. ECC 2018,Limassol, Cyprus, 2018, pp. 2867–2872.L. Farina and S. Rinaldi,Positive Linear Systems. Theory and Applications, John Wiley & Sons, New York, 2000.B.A. Francis,A Course in H∞Control Theory,Springer–Verlag, Berlin, 1987.R.A. Horn and C.R. Johnson,Matrix Analysis,Cambridge University Press, New York, 1985.10.1515/acsc-2017-0034D. Krokavec and A. Filasova, Stabilization of discrete-time LTI positive systems, Archives of Control Sciences, Vol. 27, No. 4, 2017, pp. 575–594.10.1155/2018/9590253D. Krokavec and A. Filasova, LMI based principles in strictly Metzlerian systems control design, Mathematical Problems in Engineering,Vol. 2018, 2018, pp. 1–14.D. Krokavec and A. Filasova, Descriptor approach in design of discrete-time fault estimators, WSEAS Transactions on Systems and Control, Vol. 13, 2018, pp. 481-490.10.1016/j.ejcon.2018.10.001D. Krokavec and A. Filasova, H∞norm principle in residual filter design for discrete-time lin-ear positive systems,European Journal of Con-trol, Vol. 45, 2019, pp. 17–29.10.1016/s0167-6911(01)00146-3P. De Leenheer and D. Aeyels, Stabilization of positive linear systems, Systems & Control Letters, Vol. 44, No. 4, 2001, pp. 259-271.10.1016/j.jfranklin.2018.04.015L.J. Liu, H.R. Karimi, and X. Zhao, New approaches to positive observer design for discrete-time positive linear system, Journal of Franklin Institute, Vol. 355, NO. 10, 2018,pp. 4336–4350.H. Lütkepohl,Handbook of Matrices, John Wiley & Sons, Chichester, 1996.10.1080/00207170210140212M.C. De Oliveira, J.C. Geromel, and J. Bernussou, Extended H2 and H∞norm characterizations and controller parametrizations for discrete-time systems,International Journal of Control, Vol. 75, No. 9, 2002, pp. 666-679.10.1016/0005-1098(93)90186-wP.L.D. Peres and J.C. Geromel, H2 control for discrete-time systems optimality and robustnes, Automatica, Vol. 29, No. 1, 1993, pp. 225–228.C.L. Phillips, H.T. Nagle, Digital Control System Analysis and Design, Prentice-Hall, Engle-wood Cliffs, 1995.R. Saragih, Bilinear control based on linear matrix inequalities, WSEAS Transactions on Mathematics, Volume 17, 2018, pp. 352-358.10.1002/asjc.1553J. Zhang, X. Zhao, R. Zhang and Y. Chen, Improved controller design for uncertain positive systems and its extension to uncertain positive switched systems, Asian Journal of Control,Vol. 20, No. 2, 2018, pp. 115.