### Abstract

It is shown that a linearly controllable and nonlinearly asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if (a) the linear subsystem is right-invertible and weakly minimum phase, and (b) the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free, and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. The weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem.

Original language | English (US) |
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Pages (from-to) | 1385-1391 |

Number of pages | 7 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 2 |

State | Published - Dec 1 1989 |

Externally published | Yes |

Event | Proceedings of the 28th IEEE Conference on Decision and Control. Part 2 (of 3) - Tampa, FL, USA Duration: Dec 13 1989 → Dec 15 1989 |

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*2*, 1385-1391.