Finite-time control of discrete-time linear systems

• Published in: IEEE transactions on automatic control Vol. 50; no. 5; pp. 724 - 729
• Main Authors: Amato, F., Ariola, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic stability; Biomedical engineering; Computer science; control theory; systems; Control systems; Control theory. Systems; Exact sciences and technology; Finite-time stability; Linear feedback control systems; Linear matrix inequalities; Linear systems; Lyapunov method; Output feedback; State feedback; Sufficient conditions; State feedback; Finite-time stability; Stabilization; Saturation; Discrete time; Linear matrix inequality; Feedback regulation; Linear time; Feasibility; linear systems; Linear control; Output feedback
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2005.847042

In this note, we consider the finite-time stabilization of discrete-time linear systems subject to disturbances generated by an exosystem. Finite-time stability can be used in all those applications where large values of the state should not be attained, for instance in the presence of saturations. The main result provided in the note is a sufficient condition for finite-time stabilization via state feedback. This result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite-time stability. All the conditions are then reduced to feasibility problems involving linear matrix inequalities (LMIs). Some numerical examples are presented to illustrate the proposed methodology.