On the stability properties of linear dynamic time-varying unforced systems involving switches between parameterizations from topologic considerations via graph theory

Discrete Applied Mathematics

Volumn 155, Issue 1, 2007, Pages 7-25

  De la Sen, M ^a   Ibeas, A ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

Discrete mathematics; Graph theory; Stability; Time varying systems

Indexed keywords

GRAPH THEORY; SET THEORY; STABILITY;

AXIOMATIC CONTEXT; DISCRETE MATHEMATICS; ISOLATED PARAMETERIZATIONS; TIME-VARYING SYSTEMS;

MATHEMATICAL TECHNIQUES;

EID: 33750439849     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2006.05.003     Document Type: Article

References (33)

1. Alastruey C.F. Stabilizability of systems with two point delays by using a generalized PD controller. Appl. Math. Lett. 11 4 (1998) 39-42
2. Alonso-Quesada S., and De la Sen M. Robust adaptive stabilizer of a class of time-varying plants using multiple controllers. Math. Comput. Simul. 63 1 (2003) 15-34
3. Alonso-Quesada S., and De la Sen M. Robust adaptive control with multiple estimation models for stabilization of a class of non-inversely stable time-varying plants. Asian J. Control 6 1 (2004) 59-73
4. Bakule L., Paulet-Crainiceanu F., Rodellar J., and Rossell J.M. IEEE Trans. Control Systems Technol. 13 4 (2005) 663-669
5. Buratti M. Existence of 1-rotational k-cycle systems of the complete graph. Graphs Combin. 20 1 (2004) 41-46
6. Bryant V. A characterization of some 2-connected graphs and a comment on an algorithmic proof of Brook's theorem. Discrete Math. 22 (1978) 81-83
7. Carvallo R.E., and Klir G.J. Reconstructability analysis-evaluation of reconstruction by hypotheses. Internat. J. Gen. Systems 7 1 (1981) 7-32
8. Chvatal V., and Erdos P. A note on Hamiltonian circuits. Discrete Math. 2 (1972) 111-113
9. De la Sen M. Robust stability of a class of linear time-varying systems. IMA J. Math. Control Inform. 19 4 (2002) 399-418
10. M. De la Sen, Adaptive control of single-input single-output hybrid systems possessing interacting discrete and continuous-time dynamics, Discrete Dyn. Nature Soc. (3) (2005) 299-329.
11. De la Sen M., Minambres J.J., Garrido A.J., Almansa A., and Soto J.C. Basic theoretical results for expert systems, Application to the supervision of adaptation transients in planar robots. Artificial Intelligence 152 2 (2004) 173-211
12. De la Sen M., and Luo N. On the uniform exponential stability of a wide class of linear time-delay systems. J. Math. Anal. Appl. 289 2 (2004) 456-476
13. Deo N., Prabha G.M., and Krishnamoorthy M.S. Algorithms for generating fundamental cycles in a graph. ACM Trans. Math. Software 8 (1988) 26-42
14. Gao Z.W., Liu W.Q., and So A.T.P. Decentralized control of generalized systems via a frequency domain approach. Asian J. Control 6 1 (2004) 46-58
15. Hinrischen G., and Pritchard A.J. Robust exponential stability of time-varying linear systems. Internat. J. Robust Nonlinear Control 3 1 (1993) 63-83
16. Hoang C.H., and McDiarmid C. On the divisibility of graphs. Discrete Math. 242 (2002) 145-156
17. Ibeas A., and De la Sen M. Representations of multi-model based controllers by using artificial intelligence tools. Informatica 15 3 (2004) 337-362
18. Ibeas A., De la Sen M., and Alonso-Quesada S. Intelligent control of discrete linear systems based on a supervised adaptive multiestimation scheme. J. Intelligent Robotic Systems 40 4 (2004) 359-411
19. Ibeas A., De la Sen M., and Alonso-Quesada S. Stable multi-estimation model for single-input single-output discrete adaptive control systems. Internat. J. Systems Sci. 35 8 (2004) 479-501
20. Johnson D.S., Lenstra K.J., and Kan Rinnooy A.H.G. The complexity of the network design problem. Networks 8 (1978) 279-285
21. Jungnickel D. Graph, Networks and Algorithms (1998), Springer, Berlin, Heidelberg, New York
22. Klir G.J. Foundations of fuzzy set theory and fuzzy logic: a historical overview. Internat. J. Gen. Systems 30 2 (2001) 91-132
23. Luo N.S., De la Sen M., and Rodellar J. Robust stabilization of a class of uncertain time delay systems in sliding mode. Internat. J. Robust Nonlinear Control 7 1 (1997) 59-74
24. Melin P., and Castillo O. A new method for adaptive control of non-linear plants using type-2 fuzzy logic and neural networks. Internat. J. Gen. Systems 33 2-3 (2004) 289-304
25. Mielikainen T. Frequency-based views to pattern collections. Discrete Appl. Math. 154 7 (2006) 1113-1139
26. Mihok P. On vertex partition numbers of graphs. In: Fiedler (Ed). Graphs and Other Combinatorial Topics (1983), Teubner, Leipzig 183-188
27. Narendra K.S., and Balakrishnan J. Adaptive control using multiple models. IEEE Trans. Automat. Control 42 2 (1997) 171-187
28. Nikolov N.S., and Tarassov A. Graph layering by promotion of nodes. Discrete Appl. Math. 154 5 (2006) 848-860
29. Niu Y., Lam J., Wang X., and Ho D.W.C. Observer-based sliding mode control for nonlinear state-delayed systems. Internat. J. Systems Sci. 35 2 (2004) 139-150
30. Resconi G., Klir G.J., and Stclair U. Hierarchical uncertainty metatheory based upon modal logic. Internat. J. Gen. Systems 21 1 (1992) 23-50
31. Sajna M. Cycle decompositions III: complete graphs and fixed length cycles. J. Combin. Des. 10 (2002) 27-78
32. Shalaby N. Skolem sequences. In: Colbourn C.J., and Dinitz J.H. (Eds). CRC Handbook of Combinatorial Designs. Graphs and Other Combinatorial Topics (1996), CRC Press, Boca Raton, FL 457-461
33. Zheng F., and Frank P.M. Finite dimensional variable structure control design for distributed delay systems. Internat. J. Control 74 4 (2001) 398-408