### 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) |
---|---|

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 |

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 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

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

*2*, 1385-1391.

}

*Proceedings of the IEEE Conference on Decision and Control*, vol. 2, pp. 1385-1391.

**Global stabilization of partially linear composite systems.** / Saberi, A.; Kokotovic, P. V.; Sussmann, H. J.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Global stabilization of partially linear composite systems

AU - Saberi, A.

AU - Kokotovic, P. V.

AU - Sussmann, H. J.

PY - 1989/12/1

Y1 - 1989/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0024930752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024930752&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0024930752

VL - 2

SP - 1385

EP - 1391

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -