Summary
There is an effective way of constructing a Lyapunov function without recourse to a state space construction. This is based upon an integral of special type called a path integral, and this approach is particularly suited for behavior theory. The theory successfully exhibits a deep connection between Lyapunov theory and Bézoutians. This paper extends the theory to a class of distributed parameter systems called pseudorational. A new construction of Lyapunov functions via an infinite-dimensional version of Bézoutians is presented. An example is given to illustrate the theory.
This research is supported in part by the JSPS Grant-in-Aid for Scientific Research (B) No. 18360203, and Grant-in-Aid for Exploratory Research No. 1765138. The SISTA-SMC research program is supported by the Research Council KUL: GOA AMBioRICS, CoE EF/05/006 Optimization in Engineering (OPTEC), IOF-SCORES4CHEM, several PhD/postdoc and fellow grants; by the Flemish Government: FWO: PhD/postdoc grants, projects G.0452.04 (new quantum algorithms), G.0499.04 (Statistics), G.0211.05 (Nonlinear), G.0226.06 (cooperative systems and optimization), G.0321.06 (Tensors), G.0302.07 (SVM/Kernel, research communities (ICCoS, ANMMM, MLDM)); and IWT: PhD Grants, McKnow-E, Eureka-Flite; by the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, Dynamical systems, control and optimization, 2007-2011); and by the EU: ERNSI.
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Yamamoto, Y., Willems, J.C. (2010). Path Integrals and Bézoutians for a Class of Infinite-Dimensional Systems. In: Hu, X., Jonsson, U., Wahlberg, B., Ghosh, B. (eds) Three Decades of Progress in Control Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11278-2_24
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