Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks. (English) Zbl 0877.93095

Summary: We show that a linear discrete-time system subject to input saturation is semi-globally exponentially stabilizable via linear state and/or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable, and has all its poles located inside or on the unit circle. Furthermore, the semi-globally stabilizing feedback laws are explicitly constructed. The results presented here are parallel to our earlier results on the continuous-time counterpart (Lin and Saberi, 1993).


93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
Full Text: DOI


[1] Aizerman, M.A.; Gantmacher, F.R., Absolute stability of regulator systems, (1964), Holden-Day San Francisco, CA · Zbl 0123.28401
[2] Anderson, B.D.O.; Moore, J.B., Linear optimal control, (1971), Prentice-Hall Englewood Cliffs, NJ · Zbl 0169.21902
[3] Chen, C.T., Linear system theory and design, (1984), Holt, Rinehart and Winston New York
[4] Chou, J.-H., Stabilization of linear discrete-time systems with actuator saturation, Systems control lett., 17, 141-144, (1991) · Zbl 0747.93053
[5] Fuller, A.T., In the large stability of relay and saturated control systems with linear controllers, Int. J. control, 15, 486-505, (1977)
[6] Kailath, T., Linear systems, (1980), Prentice-Hall Englewood Cliffs, NJ · Zbl 0458.93025
[7] Lin, Z., Global and semi-global control problems for linear systems subject to input saturation and minimum-phase input-output linearizable systems, ()
[8] Lin, Z.; Saberi, A., Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks, Systems control lett., 21, 225-239, (1993) · Zbl 0788.93075
[9] Narendra, K.S.; Taylor, J.H., Frequency domain criteria for absolute stability, (1973), Academic Press New York · Zbl 0266.93037
[10] Popov, V.M., Hyperstability of control systems, (1973), Springer Berlin · Zbl 0276.93033
[11] Schmitendorf, W.E.; Barmish, B.R., Null controllability of linear systems with constrained controls, SIAM J. control optim., 18, 327-345, (1980) · Zbl 0457.93012
[12] Sontag, E.D., An algebraic approach to bounded controllability of linear systems, Int. J. control, 39, 181-188, (1984) · Zbl 0531.93013
[13] Sontag, E.D.; Sussmann, H.J., Nonlinear output feedback design for linear systems with saturating controls, (), 3414-3416
[14] Sontag, E.D.; Yang, Y., Global stabilization of linear systems with bounded feedback, ()
[15] Sussmann, H.J.; Yang, Y., On the stabilizability of multiple integrators by means of bounded feedback controls, ()
[16] Teel, A.R., Global stabilization and restricted tracking for multiple integrators with bounded controls, Systems control lett., 18, 165-171, (1992) · Zbl 0752.93053
[17] Yang, Y., Global stabilization of linear systems with bounded feedback, ()
[18] Y. Yang, Private communications, 1993.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.