μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time

International Journal of Control

Volumn 82, Issue 2, 2009, Pages 378-388

  Zhang, Lixian ^a   Boukas, El Kebir ^a   Shi, Peng ^b,c,d  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^b UNIVERSITY OF GLAMORGAN   (United Kingdom)

^c VICTORIA UNIVERSITY   (Australia)

^d UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Average dwell time; Linear matrix inequalities; Model reduction; Switched linear systems

Indexed keywords

CONTINUOUS TIME SYSTEMS; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; STABILITY CRITERIA; SWITCHING SYSTEMS; UNCERTAIN SYSTEMS;

AVERAGE DWELL TIME; DISCRETE-TIME; DISCRETE-TIME SWITCHED SYSTEMS; EXISTENCE CONDITIONS; EXPONENTIALLY STABLES; MODEL ERRORS; MODEL REDUCTION; MODEL REDUCTION PROBLEMS; NUMERICAL EXAMPLES; POLYTOPIC UNCERTAIN; REDUCED MODELS; REDUCED-ORDER MODELS; SWITCHED LINEAR SYSTEMS; SWITCHING SIGNALS; THEORETICAL RESULTS;

LINEAR MATRIX INEQUALITIES;

EID: 60749084774     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170802126856     Document Type: Article

References (27)

1. Basin, M.V., and Rodkina, A.E. (2005), 'On Delay-dependent Stability for a Class of Nonlinear Stochastic Delaydifference Equations', Dynamics of Continuous. Discrete and Impulsive Systems, 12, 663-675.
2. Basin, M.V., and Rodkina, A.E. (2008), 'On Delay-dependent Stability for a Class of Nonlinear Stochastic Systems with Multiple State Delays', Nonlinear Analysis: Theory, Methods & Applications, 68, 2147-2157.
3. Branicky, M.S. (1998), 'Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems', IEEE Transactions on Automatic Control, 43, 475-782.
4. Daafouz, J., Riedinger, P., and Iung, C. (2002), 'Stability Analysis and Control Synthesis for Switched Systems: A Switched Lyapunov Function Approach', IEEE Transactions on Automatic Control, 47, 1883-1887.
5. De Koning, W. (2003), 'Digital Optimal Reduced-order Control of Pulse-width-modulated Switched Linear Systems', Automatica, 39, 1997-2003.
6. Ferrari-Trecate, G., Cuzzola, F.A., Mignone, D., and Morari, M. (2002), 'Analysis of Discrete-time Piecewise Affine and Hybrid Systems', Automatica, 38, 2139-2146.
7. 2-induced Gains of Switched Linear Systems', in Open Problems in Mathematical Systems Theory and Control, eds. V.D. Blondel, E.D. Sontag, M. Vidyasagar, and J.C. Willems, London: Springer, pp. 45-47.
8. Hespanha J.P., and Morse A.S. (1999) 'Stability of Switched Systems with Average Dwell Time,' In Proceedings 38th Conf. Decision Control, IEEE Conf. Decision Control: Phoenix, AZ, pp. 2655-2660.
9. Imura, J. (2003), 'Well-posedness Analysis of Switch-driven Piecewise Affine Systems', IEEE Transactions on Automatic Control, 48, 1926-1935.
10. Johansson, M., and Rantzer, A. (1998), 'Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems', IEEE Transactions on Automatic Control, 43, 555-559.
11. Lee, S.H., and Lim, J.T. (2000), 'Switching Control of H∞ Gain Scheduled Controllers in Uncertain Nonlinear Systems', Automatica, 36, 1067-1074.
12. Liberzon, D. (2003), Switching in Systems and Control, Boston, MA: Birkhauser.
13. McClamroch, N.H., and Kolmanovsky, I. (2000), 'Performance Benefits of Hybrid Control Design for Linear and Nonlinear Systems', IEEE Proceedings, 88, 1083-1096.
14. Morse, A.S. (1997), Control using Logic-based Switching, Heidelberg, Germany: Springer-Verlag.
15. Persis, C.D., Santis, R.D., and Morse, A.S. (2003), 'Switched Nonlinear Systems with State-dependent Dwell-time', Systems & Control Letters, 50, 291-302.
16. Rantzer, A., and Johansson, M. (2000), 'Piecewise Linear Quadratic Optimal Control', IEEE Transanctions on Automatic Control, 45, 629-637.
17. Rodkina, A.E., and Basin, M.V. (2006), 'On Delay-dependent Stability for a Class of Nonlinear Stochastic Delaydifferential Equations', Mathematics of Control, Signals and Systems, 18, 187-197.
18. Rodkina, A.E., and Basin, M.V. (2007), 'On Delay-dependent Stability for Vector Nonlinear Stochastic Delaydifference Equations with Volterra Diffusion Term', Systems & Control Letters, 56, 423-430.
19. Sun, Z.D. (2006), 'Combined Stabilising Strategies for Switched Linear Systems', IEEE Transactions on Automatic Control, 50, 666-674.
20. Tanikawa, A. (2008), 'On New Smoothing Algorithms for Discrete-time Linear Stochastic Systems with Unknown Disturbances', International Journal of Innovative Computing, Information and Control, 4, 15-24.
21. Wang, R., and Zhao, J. (2007), 'Exponential Stability Analysis for Discrete-time Switched Linear Systems with Time-delay', International Journal of Innovative Computing, Information and Control, 3, 1557-1564.
22. Xu, X., and Antsaklis, P.J. (2004), 'Optimal Control of Switched Systems Based on Parameterisation of the Switching Instants', IEEE Transactions on Automatic Control, 49, 2-16.
23. Zhai, G.S., Hu, B., Yasuda, K., and Michel, A.N. (2001), 'Disturbance Attenuation Properties of Time-controlled Switched Systems', Journal of the Franklin Institute, 338, 765-779.
24. Zhang, L., Boukas, E., and Shi, P. (2007), 'Exponential H∞ Filtering for Uncertain Discrete-time Switched Linear Systems with Average Dwell Time: A μ-dependent Approach', International Journal of Robust & Nonlinear Control, in press (Doi:10.1002/rnc.1276).
25. Zhang, L., Shi, P., and Boukas, E. (2007), 'H∞ Outputfeedback Control for Switched Linear Discrete-time Systems with Time-varying Delays', International Journal of Control, 80, 1354-1365.
26. ∞ Filtering for Switched Linear Discrete Time-delay Systems with Polytopic Uncertainties', IET Control Theory Applications, 1, 722-730.
27. Zhang, L., Shi, P., Wang, C., and Gao, H. (2006), 'Robust H∞ Filtering for Switched Linear Discrete-time Systems with Polytopic Uncertainties', International Journal of Adaptive Control & Signal Processing, 20, 291-304.