Robust quantized feedback stabilization of linear systems. (English) Zbl 1153.93492
Summary: This paper investigates the feedback stabilization problem for SISO linear uncertain control systems with saturating quantized measurements. In the fixed quantization sensitivity framework, we propose a time varying control law able to effectively account for the presence of saturation, which is often the main source of instability, designed using sliding mode techniques. Such controller is proved able to stabilize the plant both in the presence and in the absence of quantization.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C05 | Linear systems in control theory |
| 93B35 | Sensitivity (robustness) |
References:
| [1] | Brockett, R. W.; Liberzon, D., Quantized feedback stabilization of linear systems, IEEE Transactions on Automatic Control, AC-45, 7, 1279-1289 (2000) · Zbl 0988.93069 |
| [2] | Bullo, F.; Liberzon, D., Quantized control via locational optimization, IEEE Transactions on Automatic Control, AC-51, 1, 2-13 (2006) · Zbl 1366.93333 |
| [3] | Corradini, M. L.; Orlando, G., Linear unstable plants with saturating actuators: Robust stabilization by a time varying sliding surface, Automatica, 43, 1, 88-94 (2007) · Zbl 1140.93467 |
| [4] | Delchamps, D. F., Stabilizing a linear system with quantized state feedback, IEEE Transactions on Automatic Control, AC-35, 916-924 (1990) · Zbl 0719.93067 |
| [5] | Edwards, C.; Spurgeon, S. K., Sliding mode stabilization of uncertain systems using only output information, International Journal of Control, 59, 5, 1211-1229 (1995) |
| [6] | Elia, N.; Mitter, K., Stabilization of linear systems with limited information, IEEE Transactions on Automatic Control, AC-46, 9, 1384-1400 (2001) · Zbl 1059.93521 |
| [7] | Emelyanov, S. V.; Korovin, S. K.; Mamedov, I. G., Variable structure control systems: Discrete and digital (1995), Mir Publishers: Mir Publishers Moscow · Zbl 0939.93500 |
| [8] | Fagnani, F.; Zampieri, S., Stability analysis and synthesis for scalar linear systems with a quantized feedback, IEEE Transactions on Automatic Control, AC-48, 8, 1569-1584 (2003) · Zbl 1364.93561 |
| [9] | Feng, X.; Loparo, K. A., Active probing for information in control systems with quantized state measurements: A minimum entropy approach, IEEE Transactions on Automatic Control, AC-42, 216-238 (1997) · Zbl 0870.93038 |
| [10] | Fu, M. (2003). Robust stabilization of linear uncertain systems via quantized feedback. In Proc. 42th IEEE conf. on decision and control; Fu, M. (2003). Robust stabilization of linear uncertain systems via quantized feedback. In Proc. 42th IEEE conf. on decision and control |
| [11] | Fu, M.; Xie, L., On control of linear systems using quantized feedback, (Proc. 2003 American control conf., vol. 6 (2003)), 4567-4572 |
| [12] | Lee, K. S.; Haddad, A. H., Stabilization of stochastic quantized control systems, (Proc. 1999 American control conf., vol. 2 (1999)), 965-969 |
| [13] | Liberzon, D., Hybrid feedback stabilization of linear systems with quantized signals, Automatica, 39, 1543-1554 (2003) · Zbl 1030.93042 |
| [14] | Sznaier, M.; Damborg, M. J., Control of constrained discrete time linear systems using quantized controls, Automatica, 25, 623-628 (1989) · Zbl 0694.93002 |
| [15] | Turner, M. C.; Postlethwaite, I., Nonlinear regulation in constrained input discrete-time linear systems, International Journal of Control, 77, 15, 1330-1342 (2004) · Zbl 1077.93028 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
