Weak Input-to-State Stability Properties for Navigation Function Based Controllers
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Due to topological constraints, Navigation Functions, are not, except from trivial cases, equivalent to quadratic Lyapunov functions, hence systems based on Navigation Functions cannot directly accept an Input-to-State stability (ISS) characterization. However a relaxed version of Input-to-State stability, namely almost global ISS (aISS), is shown to be applicable. The proposed framework provides compositional capability for navigation function based systems. Cascade as well as feedback interconnections of aISS navigation systems are shown to also possess the aISS property under certain assumptions on the interconnections. Several simulated examples of navigation systems are presented to demonstrate the effectiveness of the proposed scheme.
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Copyright 2006 IEEE. Reprinted from 45th IEEE Conference on Decision and Control, San Diego, California, USA, December 2006. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.