An appropriate notion for stability studies of dynamical systems with a continuum of equilibria is semistability. One approach to semistability investigation is based on the nontangency between the vector field and the set of equilibria. In this work, we introduce a novel way of verifying nontangency by computing an outer estimate of the direction cone and illustrate its application through two well-known second-order systems. The stable equilibria of both the systems are shown to possess the semistability property.
Semistability Analysis of the Chaplygin Sleigh and Nonsmooth Mechanical Oscillator
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 14, 2013; final manuscript received January 29, 2014; published online March 11, 2014. Assoc. Editor: Prashant Mehta.
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Pushpak, N. S., Mahindrakar, A. D., and Ekbote, A. (March 11, 2014). "Semistability Analysis of the Chaplygin Sleigh and Nonsmooth Mechanical Oscillator." ASME. J. Dyn. Sys., Meas., Control. May 2014; 136(3): 034505. https://doi.org/10.1115/1.4026653
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