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Density Functions for Navigation-Function-Based Systems

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2 Author(s)
Loizou, S.G. ; Naval Archit. & Marine Eng. Dept., Nat. Tech. Univ. of Athens, Athens ; Jadbabaie, A.

In this paper, we present a scheme for constructing density functions for systems that are almost globally asymptotically stable (i.e., systems for which all trajectories converge to an equilibrium except for a set of measure zero) using navigation functions (NFs). Although recently-proven converse theorems guarantee the existence of density functions for such systems, such results are only existential and the construction of a density function for almost globally asymptotically stable systems remains a challenging task. We show that for a specific class of dynamical systems that are defined based on an NF, a density function can be easily derived from the system's underlying NF.

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Automatic Control, IEEE Transactions on  (Volume:53 ,  Issue: 2 )