Geodesic
Global asymptotic stabilization of bilinear control systems with periodic coefficients
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2012), pp. 17-27

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Sufficient conditions for uniform global asymptotic stabilization of the origin are obtained for bilinear control systems with periodic coefficients. The proof is based on the use of the Krasovsky theorem on global asymptotic stability of the origin for periodic systems. The stabilizing control function is feedback control constructed as the quadratic form of the phase variables and depends on time periodically.
Keywords: global asymptotic stability, stabilization, Lyapunov function, bilinear systems, periodic systems. 
@article{VUU_2012_2_a1,
     author = {V. A. Zaitsev},
     title = {Global asymptotic stabilization of bilinear control systems with periodic coefficients},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {17--27},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2012_2_a1/}
}
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V. A. Zaitsev. Global asymptotic stabilization of bilinear control systems with periodic coefficients. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2012), pp. 17-27. http://geodesic.mathdoc.fr/item/VUU_2012_2_a1/