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**Triangular configuration of uncertain systems stabilizable by means of feedback controller.**
*(English)*
Zbl 1034.93051

The paper deals with a class of controlled linear systems with coefficients involving some nonrandom uncertainties. It is assumed that in the case of zero time lag and constant parameters, the system is controllable and observable, whatever values the uncertainties of the system may take within the given ranges. It is shown that, in such a case, the system necessarily has a triangular configuration, stabilizable by means of a state variable feedback controller.

Reviewer: Guy Jumarie (MontrĂ©al)

### MSC:

93D15 | Stabilization of systems by feedback |

93B10 | Canonical structure |

93C23 | Control/observation systems governed by functional-differential equations |

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\textit{T. Amemiya}, Appl. Math. Comput. 120, No. 1--3, 45--54 (2001; Zbl 1034.93051)

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### References:

[1] | Amemiya, T.; Leitmann, G., A method for designing a stabilizing control for a class of uncertain linear delay systems, Dynamics and control, 4, 2, (1994) · Zbl 0800.93951 |

[2] | Amemiya, T., A stabilizing control for a class of uncertain linear delay systems with limited measurable state variables, Dynamics and control, 7, 3, 235-262, (1997) · Zbl 0881.93068 |

[3] | Wei, K., Quadratic stability of linear systems with structural independent time-varying uncertainties, IEEE trans. on automatic control, 35, 3, (1990) |

[4] | Petersen, I.R., Notions of stabilizability and controllability for a class of uncertain linear systems, Int. J. control, 46, 2, 409-422, (1987) · Zbl 0625.93010 |

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