Guaranteed properties of gain scheduled control for linear parameter- varying plants.

*(English)*Zbl 0754.93022Summary: Gain scheduling has proven to be a successful design methodology in many engineering applications. However in the absence of a sound theoretical analysis, these designs come with no guarantees on the robustness, performance, or even nominal stability of the overall gain scheduled design.

This paper presents such an analysis for one type of gain schedule system, namely, a linear parameter-varying plant scheduling on its exogenous parameters. Conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain schedule design. These conditions confirm and formalize popular notions regarding gain scheduled design, such as the scheduling variable should “vary slowly”.

This paper presents such an analysis for one type of gain schedule system, namely, a linear parameter-varying plant scheduling on its exogenous parameters. Conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain schedule design. These conditions confirm and formalize popular notions regarding gain scheduled design, such as the scheduling variable should “vary slowly”.

##### MSC:

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93C15 | Control/observation systems governed by ordinary differential equations |

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\textit{J. S. Shamma} and \textit{M. Athans}, Automatica 27, No. 3, 559--564 (1991; Zbl 0754.93022)

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##### References:

[1] | Burton, T.A., () |

[2] | Callier, F.M.; Desoer, C.A., An algebra of transfer functions of distributed linear time-invariant systems, IEEE trans. circ. syst., CAS-25, 651-662, (1978) · Zbl 0418.93037 |

[3] | Chen, M.J.; Desoer, C.A., Necessary and sufficient condition for robust stability of linear distributed feedback systems, Int. J. control, 35, 255-267, (1982) · Zbl 0489.93041 |

[4] | Corduneanu, C., Some differential equations with delay, (), 105-114 |

[5] | Corduneanu, C.; Lakshmikantham, V., Equations with unbounded delay: A survey, Nonlinear anal. theory methods appl., 4, 831-877, (1980) · Zbl 0449.34048 |

[6] | Corduneanu, C.; Luca, N., The stability of some feedback systems with delay, J. math. anal. applic., 51, 377-393, (1975) · Zbl 0312.34051 |

[7] | Desoer, C.A., Slowly varying system \( ẋ = A(t) x\), IEEE trans. aut. control, AC-14, 780-781, (1969) |

[8] | Desoer, C.A.; Vidyasagar, M., () |

[9] | Doyle, J., Analysis of feedback systems with structural uncertainties, (), 242-250, Part D |

[10] | Doyle, J.C.; Stein, G., Multivariable feedback design: concepts for a classical/modern synthesis, IEEE trans. aut. control, AC-26, 4-16, (1981) · Zbl 0462.93027 |

[11] | Doyle, J.C.; Wall, J.E.; Stein, G., Performance and robustness analysis for structural uncertainty, (), 629-636 |

[12] | Driver, R.D., () |

[13] | Hale, J., () |

[14] | Luca, N., The stability of the solutions of a class of integrodifferential systems with infinite delays, J. math. anal. applics., 67, 323-339, (1979) · Zbl 0415.45008 |

[15] | Miller, R.K., () |

[16] | Shamma, J.S.; Athans, M., Guaranteed properties of nonlinear gain scheduled control systems, () · Zbl 0754.93022 |

[17] | Shamma, J.S.; Athans, M., Analysis of nonlinear gain scheduled control systems, IEEE trans. aut. control, 35, 898-907, (1990) · Zbl 0723.93022 |

[18] | Stein, G.; Hartmann, G.L.; Hendrick, R.C., Adaptive control laws for F-8 flight test, IEEE trans. aut. control, AC-22, 758-767, (1977) |

[19] | Stein, G., Adaptive flight control—a pragmatic view, () |

[20] | Willems, J.C., () |

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