A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models

• Published in: IEEE transactions on automatic control Vol. 49; no. 7; pp. 1103 - 1122
• Main Authors: Nesic, D., Teel, A.R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Australia Council; Computer science; control theory; systems; Control design; Control theory. Systems; Exact sciences and technology; Feedback control; Hardware; Lyapunov method; Military computing; Robustness; Sampling methods; Stability; Sufficient conditions; Sampled system; Compact space; Stabilization; Discrete time; Non linear control; Control synthesis; Continuous time; Discontinuous control; Sampling; Differential inclusion; Modeling
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2004.831175

A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.