This paper considers input-to-state stability (ISS) analysis of discrete-time systems using continuous Lyapunov functions. The contributions are as follows. Firstly, the existence of a continuous Lyapunov function is related to inherent input-to-state stability on compact sets with respect to both inner and outer perturbations. If the Lyapunov function is K8 - continuous, this result applies to unbounded sets as well. Secondly, continuous control Lyapunov functions are employed to construct input-to-state stabilizing control laws for discrete-time systems subject to bounded perturbations. The goal is to design a receding horizon control scheme that allows the optimization of the ISS gain along a closed-loop trajectory.
|Title of host publication||Proceedings of the UKACC International Conference on Control, 7-10 September 2010, Coventry, United Kingdom|
|Place of Publication||London|
|Publisher||Institution of Engineering and Technology (IET)|
|Publication status||Published - 2010|
Lazar, M., Heemels, W. P. M. H., & Teel, A. R. (2010). Further input-to-state stability subtleties for discrete-time systems. In Proceedings of the UKACC International Conference on Control, 7-10 September 2010, Coventry, United Kingdom (pp. 613-619). London: Institution of Engineering and Technology (IET).