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Density functions for navigation-function-based systems
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DOI：10.1109/TAC.2008.917745.png)
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Abstract
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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.
Keywords:
almost gas systems
density functions
dual Lyapunov techniques
navigation functions (NFs)
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