The stabilization of non-linear systems using the angular method are considered in this paper. Using the angular method, the system is converted into two subsystems. One is a non-linear equation on a sphere and the other is a radial differential equation. The control is designed by considering the radial subsystem. The radial control can be continuous or discontinuous depending on the structure of the input map. Whenever the input map of the radial subsystem is zero, the radial control is not accessible. In this paper methods for removing this obstacle are presented.
BanksS. P.Mathematical theories of nonlinear systems, 1998 (Prentice-Hall, London).
2.
BanksS. P.On the optimal control of nonlinear systems. Syst. Control Lett., 1986, 6(5), 337–343.
3.
NaiduD. S.Optimal control systems, 2002 (CRC Press, Boca Raton, FL).
4.
KnoblochH. W.IsidoriA.FlokerziD.Topics in control theory. DMV seminar band 22, Birkhauser, Berlin, 1993.
5.
LukyanovA. G.UtkinV. I.Method of reducing equations for dynamic systems to a regular form. Autom. Remote Control, 1981, 42, 413–420.
6.
UtkinV. I.Sliding modes in control and optimisation, 1992 (Springer-Verlag, Berlin).
7.
BanksS. P.Stabilisation of nonlinear systems using the associated angular system. 14th World IFAC Congress, Beijing, 1999.
8.
ColoniusF.KliemannW.Stability radii and Lyapunov exponents. In Control of uncertain systems (Eds HinrichsenD.MartenssonB.), 1990 (Birkhauser, Berlin), 19–55.
9.
ColoniusF.KliemannW.The Lyapunov spectrum of families of time-varying matrices. Trans. Amer. Math. Soc., 1996, 348, 4389–4407.
10.
BanksS. P.SangelajiZ.Stabilisability of nonlinear systems using the associated angular system. In Proceedings of the IASTED International Conference on Control and applications, Banff, Alberta, 2001.
