Among bilinear control systems, unconstrained symmetric systems have the most complete theory. By default, controls are piecewise constant:
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Elliott, D.L. (2009). Symmetric Systems: Lie Theory. In: Bilinear Control Systems. Applied Mathematical Sciences, vol 169. Springer, Dordrecht. https://doi.org/10.1023/b101451_2
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DOI: https://doi.org/10.1023/b101451_2
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