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- Hisakazu Nakamura, Takayuki Tsuzuki, Yoshiro Fukui, Nami Nakamura
- Systems & Control Letters
- 2013

In this paper, we will show that a system on a non-contractible manifold cannot be strongly asymptotically stabilized in Filippov’s sense, even if discontinuous feedback is used. The fact is well-known for C feedback case, and we extend it to the discontinuous feedback case. To consider the stabilization problem on a non-contractible manifold, the… (More)

The purpose of this paper is searching for control Lyapunov-Morse functions(CLMF) using genetic programming(GP) for one-input-affine systems on general manifolds. The CLMF is an extended control Lyapunov function(CLF) to have multiple critical points. It is shown that a C global stabilizer is derived from a CLF for the system. As in the case of CLF, a… (More)

- T. Tsuzuki, Y. Yamashita
- 2008

The purpose of this paper is to solve a global asymptotic stabilization problem for a nonlinear control system on a Riemannian manifold. As well known, a system on a noncontractible manifold is not globally asymptotically stabilizable via a C feedback law. This problem results from the existence of multiple singular points of such a controlled system. It is… (More)

It is known that if state spaces of control systems are not contractible, the systems are not globally asymptotically stabilizable by using C feedback laws. We set multiple singular points of a flow to solve the topological obstruction. Given Morse functions satisfying conditions of the control Lyapunov function except for the singular points, this paper… (More)

This paper proposes a recursive method of constructing weak-control-Lyapunov functions for nonlinear systems. Lyapunov function is one of effective tools to study stability and stabilization in nonlinear system control design. However, a general way of finding Lyapunov functions has not been known yet. Our method is introduced by an explicit… (More)

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