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Stability for time varying linear dynamic systems on time scales. (English) Zbl 1064.39005
The author discusses the solutions of a time varying linear dynamic system of the form $x^\Delta (t)=A(t)x(t).$ Sufficient conditions for stability are given, and an instability criterion is developed.

39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
Full Text: DOI
[1] Agarwal, R.: Difference equations and inequalities. (1992) · Zbl 0925.39001
[2] Agarwal, R.; Bohner, M.; O’regan, D.; Peterson, A.: Dynamic equations on time scalesa survey. J. comput. Appl. math. 141, 1-26 (2002) · Zbl 1020.39008
[3] Bellman, R.: Introduction to matrix analysis. (1970) · Zbl 0216.06101
[4] Bohner, M.; Peterson, A.: Advances in dynamic equations on time scales. (2003) · Zbl 1025.34001
[5] Bohner, M.; Peterson, A.: Dynamic equations on time scales. (2001) · Zbl 0978.39001
[6] Brogan, W. L.: Modern control theory. (1991) · Zbl 0747.93001
[7] Chen, C. T.: Linear system theory and design. (1999)
[8] Desoer, C. A.: Slowly varying x˙=$A(t)$x. IEEE trans. Automat. control 14, 780-781 (1969)
[9] Desoer, C. A.: Slowly varying xi+1=Aixi. Electron. lett. 6, 339-340 (1970)
[10] Gard, T.; Hoffacker, J.: Asymptotic behavior of natural growth on time scales. Dynam. systems appl. 12, 131-147 (2003) · Zbl 1049.39022
[11] I.A. Gravagne, J.M. Davis, J.J. DaCunha, A unified approach to discrete and continuous high-gain adaptive controllers using time scales, submitted for publication. · Zbl 1184.93100
[12] I.A. Gravagne, J.M. Davis, J.J. DaCunha, R.J. Marks II, Bandwidth reduction for controller area networks using adaptive sampling, Proceedings of the International Conference on Robotics and Automation, New Orleans, LA, April 2004, pp. 5250 -- 5255.
[13] Hahn, W.: Stability of motion. (1967) · Zbl 0189.38503
[14] Hilger, S.: Analysis on measure chains --- a unified approach to continuous and discrete calculus. Results math. 18, 18-56 (1990) · Zbl 0722.39001
[15] S. Hilger, Ein Masskettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. Thesis, Universität Würzburg, 1988. · Zbl 0695.34001
[16] Ilchmann, A.; Owens, D. H.; Prätzel-Wolters, D.: High-gain robust adaptive controllers for multivariable systems. Systems control lett. 8, 397-404 (1987) · Zbl 0632.93046
[17] Ilchmann, A.; Ryan, E. P.: On gain adaptation in adaptive control. IEEE trans. Automat. control 48, 895-899 (2003)
[18] Ilchmann, A.; Townley, S.: Adaptive sampling control of high-gain stabilizable systems. IEEE trans. Automat. control 44, 1961-1966 (1999) · Zbl 0956.93056
[19] Kalman, R. E.; Bertram, J. E.: Control system analysis and design via the second method of Lyapunov icontinuous-time systems. Trans. ASME ser. D. J. Basic eng. 82, 371-393 (1960)
[20] Kalman, R. E.; Bertram, J. E.: Control system analysis and design via the second method of Lyapunov iidiscrete-time systems. Trans. ASME ser. D. J. Basic eng. 82, 394-400 (1960)
[21] Kelly, W.; Peterson, A.: Difference equationsan introduction with applications. (2001)
[22] Lyapunov, A. M.: The general problem of the stability of motion. Internat. J. Control 55, 521-790 (1992) · Zbl 0786.70001
[23] Pötzsche, C.; Siegmund, S.; Wirth, F.: A spectral characterization of exponential stability for linear time-invariant systems on time scales. Discrete continuous dynamic systems 9, 1223-1241 (2003) · Zbl 1054.34086
[24] Rosenbrock, H. H.: The stability of linear time-dependent control systems. J. electron. Control 15, 73-80 (1963) · Zbl 0142.35202
[25] Rugh, W. J.: Linear system theory. (1996) · Zbl 0892.93002
[26] Solo, V.: On the stability of slowly-time varying linear systems. Math. control signals systems 7, 331-350 (1994) · Zbl 0833.93047
[27] Zhang, F.: Matrix theorybasic results and techniques. (1999)