A small gain approach to global stabilization of nonlinear feedforward systems with input unmodeled dynamics

• Published in: Automatica (Oxford) Vol. 46; no. 6; pp. 1028 - 1034
• Main Authors: Chen, Tianshi, Huang, Jie
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.06.2010; Elsevier
• Subjects: Applied sciences; Asymptotic properties; Automatic control; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Dynamical systems; Dynamics; Exact sciences and technology; Feedforward; Gain; Information technology; Informationsteknik; Nonlinear dynamics; Nonlinear system; Reglerteknik; Robust stability; TECHNOLOGY; TEKNIKVETENSKAP; Theorems; Unmodeled dynamics; Unmodeled dynamics; Nonlinear system; Robust stability; Saturation; Non linear control; Control synthesis; Jacobi matrix; Non linear system; Local effect; Closed feedback; Robust control; Asymptotic stability; Global stabilization; Small gain theorem; Recursive method; Robustness; Asymptotic approximation; Feedforward; Linearization
• ISSN: 0005-1098; 1873-2836; 1873-2836
• DOI: 10.1016/j.automatica.2010.02.028

In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system. An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics.