1. W. Liu, Y. Chitour, and E.D. Sontag. On finite-gain stabilizability of linear systems subject to input saturation. SIAM J. Control Optim., 34(4):1190-1219, 1996. [PDF] [doi:http://dx.doi.org/10.1137/S0363012994263469] Keyword(s): saturation, bounded inputs. Abstract:

   This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every Lp-norm. Explicit bounds on closed-loop gains are obtained, and they are related to the norms for the respective systems without saturation. These results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple (size >1) Jordan blocks, contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state-space sense; this is shown in particular for the double integrator.




2. Y. Chitour, W. Liu, and E.D. Sontag. On the continuity and incremental-gain properties of certain saturated linear feedback loops. Internat. J. Robust Nonlinear Control, 5(5):413-440, 1995. [PDF] Keyword(s): saturation, bounded inputs, incremental gains. Abstract:

   This paper discusses various continuity and incremental-gain properties for neutrally stable linear systems under linear feedback subject to actuator saturation. The results complement our previous ones, which applied to the same class of problems and provided finite-gain stability.

1. Y. Chitour, W. Liu, and E.D. Sontag. On the continuity and incremental gain properties of certain saturated linear feedback loops. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 127-132, 1994. [PDF] Keyword(s): saturation, bounded inputs.



2. W. Liu, Y. Chitour, and E.D. Sontag. Remarks on finite gain stabilizability of linear systems subject to input saturation. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 1808-1813, 1993. Keyword(s): saturation, bounded inputs.

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