### Abstract

In this paper, we propose a high-gain scaling based controller to achieve global state-feedback stabilization of a general class of nonlinear systems which are allowed to contain uncertain functions of all the states and the control input as long as polynomial bounds on ratios of some uncertain system terms are available. The design is based on a high-gain scaling involving appropriate powers of a high-gain scaling parameter which is a dynamic signal driven by the state. The designed controller has a very simple structure being essentially a dynamic extension and a linear feedback with state-dependent dynamic gains. The obtained results are applicable to both lower triangular (strict-feedback) and upper triangular (feedforward) structures and also to systems without any triangular structure as long as a set of inequalities involving powers of the polynomial bounds on the ratios of the uncertain system terms and scaling orders is solvable. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations.

Original language | English (US) |
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Title of host publication | Proceedings of the American Control Conference |

Pages | 3427-3432 |

Number of pages | 6 |

Volume | 5 |

State | Published - 2005 |

Event | 2005 American Control Conference, ACC - Portland, OR, United States Duration: Jun 8 2005 → Jun 10 2005 |

### Other

Other | 2005 American Control Conference, ACC |
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Country | United States |

City | Portland, OR |

Period | 6/8/05 → 6/10/05 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*(Vol. 5, pp. 3427-3432). [FrA01.4]

**Generalized state scaling-based robust control of nonlinear systems and applications to triangular systems.** / Krishnamurthy, P.; Khorrami, Farshad.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the American Control Conference.*vol. 5, FrA01.4, pp. 3427-3432, 2005 American Control Conference, ACC, Portland, OR, United States, 6/8/05.

}

TY - GEN

T1 - Generalized state scaling-based robust control of nonlinear systems and applications to triangular systems

AU - Krishnamurthy, P.

AU - Khorrami, Farshad

PY - 2005

Y1 - 2005

N2 - In this paper, we propose a high-gain scaling based controller to achieve global state-feedback stabilization of a general class of nonlinear systems which are allowed to contain uncertain functions of all the states and the control input as long as polynomial bounds on ratios of some uncertain system terms are available. The design is based on a high-gain scaling involving appropriate powers of a high-gain scaling parameter which is a dynamic signal driven by the state. The designed controller has a very simple structure being essentially a dynamic extension and a linear feedback with state-dependent dynamic gains. The obtained results are applicable to both lower triangular (strict-feedback) and upper triangular (feedforward) structures and also to systems without any triangular structure as long as a set of inequalities involving powers of the polynomial bounds on the ratios of the uncertain system terms and scaling orders is solvable. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations.

AB - In this paper, we propose a high-gain scaling based controller to achieve global state-feedback stabilization of a general class of nonlinear systems which are allowed to contain uncertain functions of all the states and the control input as long as polynomial bounds on ratios of some uncertain system terms are available. The design is based on a high-gain scaling involving appropriate powers of a high-gain scaling parameter which is a dynamic signal driven by the state. The designed controller has a very simple structure being essentially a dynamic extension and a linear feedback with state-dependent dynamic gains. The obtained results are applicable to both lower triangular (strict-feedback) and upper triangular (feedforward) structures and also to systems without any triangular structure as long as a set of inequalities involving powers of the polynomial bounds on the ratios of the uncertain system terms and scaling orders is solvable. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations.

UR - http://www.scopus.com/inward/record.url?scp=23944504500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23944504500&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:23944504500

VL - 5

SP - 3427

EP - 3432

BT - Proceedings of the American Control Conference

ER -