Nonnegativity, stability analysis of linear discrete-time positive descriptor systems: an optimization approach

• Autorzy: Yang H. , Zhou M. , Zhao M. , Pan P.

Identyfikatory

DOI

10.24425/119055

• Języki publikacji: EN

Abstrakty

EN

This paper discusses an efficient approach to the analysis of positivity and stability of linear discrete-time positive descriptor system. Irs main objective is to convert the necessary and sufficient condition of characterizing positivity and stability of positive descriptor systems into an optimization problem, then propose a method to numerically check the positivity and stability of the positive linear discrete-time systems. Comparing with the other methods now available, the approach presented in this paper is less theoretical and easier to implement. Examples are provided in order to validate results.

Słowa kluczowe

EN

descriptor systems; positive systems; positivity; stability; optimization

PL

stabilność; optymalizacja; deskryptor

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 1
• Strony: 1--7
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Yang H.

• Mathematics Department of Shandong University of Science and Technology, 266590, Qingdao Shandong, China

autor

Zhou M.

• Mathematics Department of Shandong University of Science and Technology, 266590, Qingdao Shandong, China

autor

Zhao M.

• Mathematics Department of Shandong University of Science and Technology, 266590, Qingdao Shandong, China

autor

Pan P.

• Mathematics Department of Shandong University of Science and Technology, 266590, Qingdao Shandong, China

Bibliografia

• [1] L. Dai, Sin&ilar Control Systems, Springer-Verlag, Berlin, 19S9.
• [2] M. Hou, "Controllability and elimination of impulsive modes in descriptor systems", IEEE Transactions on Automatic Control, 49(10), 1723 1727(2004).
• [3] D. Wang and C.B. Soh, "On regularizing singular systems by decentralized output feedback", IEEE Transactions on Automatic Control44 (\), 148 152 (1999).
• [4] Y. Feng and M. Yagoubi, "Comprehensive admissibility for descriptor systems", Automatica 66 (C). 271-275 (2016).
• [5] C.J. Wang, "On linear quadratic optimal control of linear time-varying singular systems", International Journal of Systems Science 35 (15), 903-906 (1999).
• [6] L.Q. Zhang, B. Huang, and J. Lam, "LMI synthesis of H2 and-mixed H2/H∞ controllers for singular systems", IEEE Transactions on Circuits and Systems-I, 50 (9), 615-626 (2003).
• [7] A.G Wu, G.R. Duan, and Y.M Fu, "Generalized PID observer design for descriptor linear systems", IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, 37 (5). 1390-1395 (2007).
• [8] Z. Yong and Z. Weihai, "Observer-based controller design for singular stochastic Markov jump systems with state dependent noise", Journal of Systems Science ana" Complexity, 29 (4), 946-958 (2016).
• [9] M. Hong-Ji and H. Ting, "A separation theorem for stochastic singular linear quadratic control problem with partial information", Acta Mathematical Applicator Sinica-English Series, 29 (2), 303-314(2013).
• [10] U. Krause, Positive Dynamical Systems in Discrete Time, Theory, Methods, and Applications, De tiruyter, Germany, 2015.
• [11] F.L. Lewis, "A survey of linear singular systems", Circuits, Systems and Signal Processing, 5 (1), 3-36 (1986).
• [12] T. Kaczorek, "Reachability and controllability of 2D positive linear systems with state feedbacks", Mull Pol. Ac.; Tech-, 47 (1), 67-73(1999).
• [13] T. Kaczorek, "Stability tests of positive conti nous-time linear systems with delays", TransNav: International Journal on Marine Navigation and Safety of Sea Trtmsportainn, 1 (2), 211- 215 (2013).
• [14] T. Kaczorek, "Asymptotic stability of positive 1D and 2D linear systems". Bull Pol Ac.: Tech., 57 (2), 67-73 (2009).
• [15] T. Kaczorek, "Practical stability and asymptotic stability of positive fractional 2D linear systems". Asian Journal of Control, 12 (2), 200 207(2010).
• [16] T. Kaczorek, "Positivily and asymptotic stability of descriptor linear systems with regular pencils", Archives of Control Sciences, 24 (2), 193-205 (2014).
• [17] E. Virnik, "Stability analysis of positive descriptor systems", Linear Algebra and its Application, 429 (10), 2640-2659 (2008).
• [18] G. James and V. Rumchev, "Stability of positive linear discrete-time systems". Bull. Pol. Ac.: Tech., 53 (1), 1 8 (2005).
• [19] A. Herrero, A- Ramirez, and N. Thome, "An algorithm to check the nonnegativity of singular systems". Applied Mathematics and Computation, 189 (1), 355 365 (2007).
• [20] T. Kaczorek, "Checking of the positivity of descriptor linear systems with singular pencils". Archives ofConiml Sciences, 22(0,77-86(2012).
• [21] Y Zhang, Q. Zhang, T Tanaka, and M. Cai, "Admissibility for positive continuous-time descriptor systems", International Journal t>j Systtm Sciences. 44 (II), 2158-2165 (2013).
• [22] M.A. Rami and D. Napp, "Characterization and stability of autonomous positive descriptor systems". IEEE Transactions on Automatic Control, 57 (10), 2668 2673 (2012).
• [23] M.A. Rami and D. Napp, "Posivity of discrete singular systems and their stability: an LP-based approach", Automatic, 50, 84 91 (2014).
• [24] F. Tao, M, Xinzhu, L. Lidan, andG. Shujing, "Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model", Journal of Inequalities and Applications, 2016(327), 1 29(2016).
• [25] W. Mitkowski "Remarks on stability of positive linear systems", Control and Cybernetics, 2') (1), 295 304 (2000).
• [26] O. Haichao, D. Wei, and M. Linli, "Positivity and stability analysis of positive discrete-time descriptor systems", Proceedings of 2016 Chinese Control and Decision Conference (CCD), Yinchuan China, 982-987 (2016).

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).