Application of 2D systems to investigation of a process of gas filtration

Multidimensional Systems and Signal Processing

Volumn 23, Issue 1-2, 2012, Pages 119-130

  Bors, Dorota ^a   Walczak, Stanisław ^a  

^a UNIVERSITY OF LODZ   (Poland)

Author keywords

Fixed point; Gas filtration; Optimal control; Two dimensional systems

Indexed keywords

2-D SYSTEMS; FIXED POINTS; GAS FILTRATION; OPTIMAL CONTROLS; OPTIMAL PROCESS; SUFFICIENT CONDITIONS; TWO-DIMENSIONAL SYSTEMS;

SIGNAL PROCESSING;

OPTIMIZATION;

EID: 84855796911     PISSN: 09236082     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11045-010-0110-7     Document Type: Article

References (24)

1. E. Berkson T. A. Gillespie 1984 Absolutely continuous functions of two variables and well-bounded operators Journal of the London Mathematical Society 2 30 305 321 10.1112/jlms/s2-30.2.305 771426
2. L. Cesari 1969 Optimization with partial differential equations in Dieudonne-Rashevsky form and conjugate problems Archive for Rational Mechanics and Analysis 33 339 357 10.1007/BF00247693 0182.20302 240695
3. Cesari L. (1983) Optimization theory and application. Springer, New York
4. M. Dymkov I. Gaishun K. Gałkowski D. H. Owens E. Rogers 2004 Control theory for a class of 2D continuous-discrete linear systems International Journal of Control 77 9 847 860 10.1080/00207170410001726796 1060.93055 2082178
5. A. I. Egorov 1966 Necessary optimality conditions for systems with distributed parameters Matematicheskii Sbornik 69 3 371 421 (Russian)
6. E. Fornasini G. Marchesini 1976 State-space realization theory of two-dimensional filters IEEE Transactions on Automatic Control AC-21 4 484 491 10.1109/TAC.1976.1101305 414239
7. E. Fornasini G. Marchesini 1978 Doubly indexed dynamical systems; state space models and structural properties Mathematical Systems Theory 12 1 59 72 10.1007/BF01776566 0392.93034 510621
8. K. Gałkowski V. Vinnikov 2004 Multidimensional control systems: Theory with a view to applications International Journal of Control 77 9 801 10.1080/00207170412331294770 2082173
9. Hildebrandt T. H. (1963) Introduction to the theory of integration. Academic Press, New York, London
10. D. Idczak S. Walczak 2000 On the existence of a solution for some distributed optimal control hyperbolic system International Journal of Mathematics and Mathematical Science 23 5 297 311 10.1155/S0161171200000880 0959.49004 1754237
11. Ioffe A. D.; Tikhomirov V. M. (1979) Theory of extremal problems. Academic Press, New York
12. Kaczorek, T. (1985). Two-dimensional linear systems. Lecture Notes in Control and Information Sciences, Springer.
13. T. Kaczorek 2000 Reachability and controllability of 2D positive linear systems with state feedbacks Control and Cybernetics 29 1 141 151 1012.93030 1775162
14. T. Kaczorek 2001 Perfect observers for singular 2-D Fornasini-Marchesini models IEEE Transactions on Automatic Control 46 10 1671 1675 10.1109/9.956070 1009.93044 1859197 (Pubitemid 33018241)
15. J. Lam S. Xu Y. Zou Z. Lin K. Gałkowski 2004 Robust output feedback stabilization for two-dimensional continuous systems in Roesser form Applied Mathematics Letters 17 12 1331 1341 10.1016/j.am1.2004.04.004 1122.93405 2103454 (Pubitemid 40114650)
16. V. Lomadze E. Rogers J. Wood 2009 Singular 2D behaviors: Fornasini-Marchesini and Givone-Roesser models Georgian Mathematical Journal 16 1 105 130 1163.93013 2527619
17. Łojasiewicz S. (1988) An introduction to the theory of real functions. Wiley, Chichester
18. Pontriagin L. S.; Boltyanskii V. G.; Gamkrelidze R. V.; Mischenko E. F. (1960) The mathematical theory of optimal processes. Interscience, New York
19. V. Rehbock S. Wang K. L. Teo 1998 Computing optimal control with a hyperbolic partial differential equation Journal of the Australian Mathematical Society Series B 40 2 266 287 10.1017/S0334270000012510 0917.65060 1668143 (Pubitemid 128757411)
20. M. B. Surryyanarayana 1973 Necessary conditions for optimization problems with hyperbolic partial differential equations SIAM Journal of Control 11 4 130 147
21. Tikhonov, A. N.; & Samarski, A. A. (1978). Equations of Mathematical Physics. Moscow.
22. S. Walczak 1984 Some properties of cones in normed spaces and their application to investigating extremal problems Journal of Optimization Theory and Applications 42 4 561 582 10.1007/BF00934567 0504.52001 739435 (Pubitemid 14562975)
23. S. Walczak 1987 Absolutely continuous functions of several variables and their applications to differential equations Bulletin of the Polish Academy of Science and Mathematics 35 11-12 733 744 0691.35029 961712
24. S. Xu J. Lam K. Gałkowski Z. Lin 2006 An LMI approach to the computations of lower bounds for stability margins of 2D discrete systems Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms 13 2 221 236 1162.93374 2204066 (Pubitemid 44965442)