On global stabilization of cascaded nonlinear systems. (English) Zbl 0736.93004
New trends in systems theory, Proc. Jt. Conf., Genoa/Italy 1990, Prog. Syst. Control Theory 7, 554-559 (1991).
Summary: [For the entire collection see Zbl 0726.00023.]
We study the problem of global smooth stabilization of cascade compositions of nonlinear globally asymptotically stable systems. Our main result is that global stabilization can be achieved if we can render the first system strictly passive for an output which spans the “unstable part” of the vector field of the second system. This result generalizes earlier stabilizability conditions for the case when the first system is linear. Also, it provides some insight on the (“energy dissipation”) properties of the dependence of the second system vector field and the first systems “output” needed to achieve global stabilization.
We study the problem of global smooth stabilization of cascade compositions of nonlinear globally asymptotically stable systems. Our main result is that global stabilization can be achieved if we can render the first system strictly passive for an output which spans the “unstable part” of the vector field of the second system. This result generalizes earlier stabilizability conditions for the case when the first system is linear. Also, it provides some insight on the (“energy dissipation”) properties of the dependence of the second system vector field and the first systems “output” needed to achieve global stabilization.
MSC:
| 93A99 | General systems theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
