Uniform stabilization of discrete-time switched and Markovian jump linear systems

Automatica

Volumn 42, Issue 2, 2006, Pages 205-218

  Lee, Ji Woong ^a,c   Dullerud, Geir E ^b,d  

^a University of Florida   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c UNIVERSITY OF FLORIDA   (United States)

^d UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Discrete linear inclusions; Dynamic output feedback; Linear matrix inequalities; Linear time varying systems; Uniform exponential stability

Indexed keywords

DISCRETE LINEAR INCLUSIONS; DYNAMIC OUTPUT FEEDBACK; LINEAR MATRIX INEQUALITIES; LINEAR TIME-VARYING SYSTEMS; UNIFORM EXPONENTIAL STABILITY;

DISCRETE TIME CONTROL SYSTEMS; FEEDBACK; LINEAR CONTROL SYSTEMS; MARKOV PROCESSES; MATRIX ALGEBRA; SWITCHING; TIME VARYING CONTROL SYSTEMS;

SYSTEM STABILITY;

EID: 29244450124     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2005.08.019     Document Type: Article

References (48)

1. A.A. Agrachev, and D. Liberzon Lie-algebraic stability criteria for switched systems SIAM Journal on Control and Optimization 40 1 2001 253 269
2. P. Apkarian, and P. Gahinet A convex characterization of gain-scheduled H ∞ controllers IEEE Transactions on Automatic Control 40 5 1995 853 864
3. F. Blanchini, and S. Miani Stabilization of LPV systems: State feedback, state estimation, and duality SIAM Journal on Control and Optimization 42 1 2003 76 97
4. Bliman, P. -A., & Ferrari-Trecate, G. (2003). Stability analysis of discrete-time switched systems through Lyapunov functions with nonminimal state. In IFAC conference on the analysis and design of hybrid systems.
5. Blondel, V. D., & Megretski, A. (Eds.) (2004). Unsolved problems in mathematical systems and control theory. Princeton, NJ: Princeton University Press.
6. V.D. Blondel, J. Theys, and A.A. Vladimirov An elementary counterexample to the finiteness conjecture SIAM Journal on Matrix Analysis and Applications 24 4 2003 963 970
7. V.D. Blondel, and J.N. Tsitsiklis NP-hardness of some linear control design problems SIAM Journal on Control and Optimization 35 6 1997 2118 2127
8. V.D. Blondel, and J.N. Tsitsiklis A survey of computational complexity results in systems and control Automatica 36 9 2000 1249 1274
9. T. Bousch, and J. Mairesse Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture Journal of the American Mathematical Society 15 1 2002 77 111
10. M.S. Branicky Multiple Lyapunov functions and other analysis tools for switched and hybrid systems IEEE Transactions on Automatic Control 43 4 1998 475 482
11. Chan, H., & Özgüner, U. (1995). Optimal control of systems over a communication network with queues via a jump system approach. In Proceedings of the 4th IEEE conference on control applications, pp. 1148-1153.
12. O.L.V. Costa, and M.D. Fragoso Stability results on discrete-time linear systems with Markovian jumping parameters Journal of Mathematical Analysis and Applications 179 1 1993 154 178
13. J. Daafouz, P. Riedinger, and C. Iung Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach IEEE Transactions on Automatic Control 47 11 2002 1883 1887
14. I. Daubechies, and J.C. Lagarias Sets of matrices all infinite products of which converge Linear Algebra and its Applications 161 1992 227 263
15. I. Daubechies, and J.C. Lagarias Corrigendum/addendum to: Sets of matrices all infinite products of which converge Linear Algebra and its Applications 327 2001 69 83
16. D.P. de Farias, J.C. Geromel, J.B.R. do Val, and O.L.V. Costa Output feedback control of Markov jump linear systems in continuous-time IEEE Transactions on Automatic Control 45 5 2000 944 949
17. G.E. Dullerud, and S. Lall A new approach for analysis and synthesis of time-varying systems IEEE Transactions on Automatic Control 44 8 1999 1486 1497
18. J. Ezzine, and D. Kavranoǧlyu On almost-sure stabilization of discrete-time jump parameter systems: An LMI approach International Journal of Control 68 5 1997 1129 1146
19. Y. Fang A new general sufficient condition for almost sure stability of jump linear systems IEEE Transactions on Automatic Control 42 3 2004 378 382
20. P. Gahinet, and P. Apkarian A linear matrix inequality approach to H ∞ control International Journal of Robust and Nonlinear Control 4 4 1994 421 448
21. L. Gurvits Stability of discrete linear inclusion Linear Algebra and its Applications 231 1995 47 85
22. J.P. Hespanha Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle IEEE Transactions on Automatic Control 49 4 2004 470 482
23. P.G. Hoel, S.C. Port, and C.J. Stone Introduction to stochastic processes 1987 Waveland Press Long Grove, IL
24. R.A. Horn, and C.R. Johnson Matrix analysis 1985 Cambridge University Press Cambridge, UK
25. Y. Ji, and H.J. Chizeck Controllability, stability, and continuous-time Markovian jump linear quadratic control IEEE Transactions on Automatic Control 35 7 1990 777 788
26. Y. Ji, H.J. Chizeck, X. Feng, and K.A. Loparo Stability and control of discrete-time jump linear systems Control - Theory and Advanced Technology 7 2 1991 247 270
27. E.W. Kamen, P.P. Khargonekar, and K.R. Poolla A transfer-function approach to linear time-varying discrete-time systems SIAM Journal on Control and Optimization 23 4 1985 550 565
28. R. Krtolica, U. Özgüner, H. Chan, H. Göktas, J. Winkelman, and M. Liubakka Stability of linear feedback systems with random communication delays International Journal of Control 59 4 1994 925 953
29. J.C. Lagarias, and Y. Wang The finiteness conjecture for the generalized spectral radius of a set of matrices Linear Algebra and its Applications 214 1995 17 42
30. J.B. Lasserre Global optimization with polynomials and the problem of moments SIAM Journal on Optimization 11 3 2001 796 817
31. J.B. Lasserre An explicit equivalent positive semidefinite program for nonlinear 0-1 programs SIAM Journal on Optimization 12 3 2002 756 769
32. D. Liberzon Switching in systems and control 2003 Birkhäuser Boston, MA
33. N. Lynch, R. Segala, and F. Vaandrager Hybrid I/O automata Information and Computation 185 1 2003 105 157
34. M. Mariton Almost sure and moments stability of jump linear systems Systems & Control Letters 11 5 1988 393 397
35. Mitra, S., & Liberzon, D. (2004). Stability of hybrid automata with average dwell time: An invariant approach. In Proceedings of the 43rd IEEE conference on decision and control (Vol. 2) (pp. 1394-1399).
36. Mori, Y., Mori, T., & Kuroe, Y. (1997). A solution to the common Lyapunov function problem for continuous-time systems. In Proceedings of the 36th IEEE conference on decision and control. (Vol. 4) (pp. 3530-3531).
37. A. Packard Gain scheduling via linear fractional transformations Systems & Control Letters 22 2 1994 79 92
38. Peleties, P., & DeCarlo, R. (1991). Asymptotic stability of m-switched systems using Lyapunov-like functions. In Proceedings of the American control conference (Vol. 2) (pp. 1679-1684).
39. K. Poolla, and P.P. Khargonekar Stabilizability and stable-proper factorizations for linear time-varying systems SIAM Journal on Control and Optimization 25 3 1987 723 736
40. K.M. Przyluski, and S. Rolewicz On the stability of linear time-varying infinite-dimensional discrete-time systems Systems & Control Letters 4 5 1984 307 315
41. M.A. Rotea, and P.P. Khargonekar Stabilizability of linear time-varying and uncertain linear systems IEEE Transactions on Automatic Control 33 9 1988 884 887
42. Schaft, A. V. D., & Schumacher, H. (2000). An introduction to hybrid dynamical systems. Lecture notes in control and information science. (Vol. 251) London, UK: Springer.
43. A.N. Shiryayev Probability 1996 Springer New York, NY
44. Spong, M. W., & Block, D. J. (1995). The Pendubot: A mechatronic system for control research and education. In Proceedings of the 34th IEEE conference on decision and control (Vol. 1) (pp. 555-556).
45. J.N. Tsitsiklis, and V.D. Blondel The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible - to compute and to approximate Mathematics of Control, Signals, and Systems 10 1 1997 31 40
46. A. Vladimirov, L. Elsner, and W.-J. Beyn Stability and paracontractivity of discrete linear inclusions Linear Algebra and its Applications 312 2000 125 134
47. Xiao, L., Hassibi, A., & How, J. P. (2000). Control with random communication delays via a discrete-time jump system approach. In Proceedings of the American control conference (Vol. 3) (pp. 2199-2204).
48. Yoo, B., 2003. Real-time control of dynamic systems over communication networks. Master's thesis, University of Illinois at Urbana-Champaign.