Stability and Robustness Analysis for Curve Tracking Control using Input-to-State Stability

• Published in: IEEE transactions on automatic control Vol. 57; no. 5; pp. 1320 - 1326
• Main Authors: Malisoff, M., Mazenc, F., Fumin Zhang
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Aerospace electronics; Applied sciences; Automatic control; Automatic Control Engineering; Computer Science; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Controllers; Delay; Exact sciences and technology; Feedback; Input-to-state stability; Invariants; Laws; Lyapunov methods; mobile robot curve tracking; Perturbation methods; Robotics; Robots; robust control; Robustness; Stability; Stability analysis; stability of NL systems; Tracking problem; Trajectory; Invariant; Moving robot; Input-to-state stability; Control program; Feedback regulation; Control synthesis; mobile robot curve tracking; Tracking task; Robotics; Robust control; Input to state stability; stability of NL systems; Robustness; Delay time; Polygon; Motion control; Output feedback; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2174664

We study an important class of feedback controllers that arise in curve tracking problems for robotics. Previous experimental results suggested the robust performance of the control laws under perturbations. Here we use input-to-state stability to prove predictable tolerance and safety bounds that ensure robust performance under perturbations and time delays. Our proofs are based on an invariant polygon argument and a new strict Lyapunov function design.