### Abstract

VSS observers are considered for continuous-time systems, in which the nominal plant model is linear, but there exist bounded plant and output uncertainties. We first present a design method of a VSS observer based on use of some extensions of a conventional approach that uses an algebraic Lyapunov equation. It is then shown that such a method cannot be successfully applied to the system with any linear part, if we desire to use a unique solution to the algebraic Lyapunov equation. Namely, this method is only applicable to a restricted class of systems. In order to develop a VSS observer applicable to a wider class of systems, we next propose a design method based on use of an algebraic Riccati equation, associated with a linear filtering problem. A relationship between the two design methods is also discussed. Simulation results show that the proposed method is effective for designing a VSS observer for a second-order nonlinear system with band limited output noise, as the output uncertainty.

Original language | English |
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Pages (from-to) | 416-424 |

Number of pages | 9 |

Journal | JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing |

Volume | 40 |

Issue number | 3 |

Publication status | Published - Sep 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Algebraic Lyapunov Equation
- Algebraic Riccati Equation
- Nonlinear Observer
- Nonlinear Systems
- Output Uncertainties
- Robust Estimation
- Variable Structure Systems (VSS)
- VSS Observer

### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering
- Mechanical Engineering
- Engineering(all)

### Cite this

**A Design Method of VSS Observer for Continuous-Time Systems with Output Uncertainties.** / Watanabe, Keigo.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A Design Method of VSS Observer for Continuous-Time Systems with Output Uncertainties

AU - Watanabe, Keigo

PY - 1997/9

Y1 - 1997/9

N2 - VSS observers are considered for continuous-time systems, in which the nominal plant model is linear, but there exist bounded plant and output uncertainties. We first present a design method of a VSS observer based on use of some extensions of a conventional approach that uses an algebraic Lyapunov equation. It is then shown that such a method cannot be successfully applied to the system with any linear part, if we desire to use a unique solution to the algebraic Lyapunov equation. Namely, this method is only applicable to a restricted class of systems. In order to develop a VSS observer applicable to a wider class of systems, we next propose a design method based on use of an algebraic Riccati equation, associated with a linear filtering problem. A relationship between the two design methods is also discussed. Simulation results show that the proposed method is effective for designing a VSS observer for a second-order nonlinear system with band limited output noise, as the output uncertainty.

AB - VSS observers are considered for continuous-time systems, in which the nominal plant model is linear, but there exist bounded plant and output uncertainties. We first present a design method of a VSS observer based on use of some extensions of a conventional approach that uses an algebraic Lyapunov equation. It is then shown that such a method cannot be successfully applied to the system with any linear part, if we desire to use a unique solution to the algebraic Lyapunov equation. Namely, this method is only applicable to a restricted class of systems. In order to develop a VSS observer applicable to a wider class of systems, we next propose a design method based on use of an algebraic Riccati equation, associated with a linear filtering problem. A relationship between the two design methods is also discussed. Simulation results show that the proposed method is effective for designing a VSS observer for a second-order nonlinear system with band limited output noise, as the output uncertainty.

KW - Algebraic Lyapunov Equation

KW - Algebraic Riccati Equation

KW - Nonlinear Observer

KW - Nonlinear Systems

KW - Output Uncertainties

KW - Robust Estimation

KW - Variable Structure Systems (VSS)

KW - VSS Observer

UR - http://www.scopus.com/inward/record.url?scp=0031223537&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031223537&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031223537

VL - 40

SP - 416

EP - 424

JO - JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing

JF - JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing

SN - 1344-7653

IS - 3

ER -