##
**Optimality of decentralized control for large-scale systems.**
*(English)*
Zbl 0646.93004

Summary: A decentralized control scheme is given for the stabilization of large- scale systems composed of a number of controllable subsystems. A class of interconnection structures among subsystems is defined for which the overall system can always be stabilized by local state feedback which is optimal for a quadratic performance index. The resulting closed-loop system has robust stability properties against a wide range of variations in open-loop dynamics. Optimality of the decentralized control law is preserved for a modified performance index under perturbations in interconnections such that the strength of coupling does not increase. The class of decentrally stabilizable large-scale systems presented in this paper is the largest such class hitherto described by the structure of interconnections.

### MSC:

93A15 | Large-scale systems |

93B35 | Sensitivity (robustness) |

93D15 | Stabilization of systems by feedback |

### Keywords:

decentralized control; stabilization; large-scale systems; local state feedback; robust stability
Full Text:
DOI

### References:

[1] | Araki, M.; Kondo, B., Stability and transient behavior of composite nonlinear systems, IEEE Trans Aut. Control, AC-17, 537 (1972) · Zbl 0275.93031 |

[2] | Corfmat, J. P.; Morse, A. S., Decentralized control of linear multivariable systems, Automatica, 12, 479 (1976) · Zbl 0347.93019 |

[3] | Davison, E. J., The decentralized stabilization and control of a class of unknown nonlinear time-varying systems, Automatica, 10, 309 (1974) · Zbl 0308.93023 |

[4] | Ikeda, M.; Šiljak, D. D., On decentrally stabilizable large-scale systems, Automatica, 16, 331 (1980) · Zbl 0432.93004 |

[5] | Ikeda, M.; Šiljak, D. D., Decentralized stabilization of large-scale systems with delay, Large Scale Systems, 1, 273 (1980) · Zbl 0464.93063 |

[6] | Ikeda, M.; Šiljak, D. D., On optimality of decentralized control with overlapping information sets, (Proc. NCKU/AAS Symposium (1981)), 51-65 |

[7] | Ikeda, M.; Umefuji, O.; Kodama, S., Stabilization of large-scale linear systems, Trans. IECE Japan (D), 59-D, 355 (1976), also in Syst. Comp. Control, 7, 34 |

[8] | Kalman, R. E., Contributions to the theory of optimal control, Boletin de la Sociedad Matematica Mexicana, 5, 102 (1960) · Zbl 0112.06303 |

[9] | Luenberger, D. G., Canonical forms for linear multivariable systems, IEEE Trans Aut. Control, AC-12, 290 (1967) |

[10] | Özgüner, Ü., Local optimization in large-scale composite dynamic systems, (Proc. 9th Asilomar Conference (1975)), 87-91 |

[11] | Safonov, M. G.; Athans, M., Gain and phase margin for multiloop LOG regulators, IEEE Trans Aut. Control, AC-22, 173 (1977) · Zbl 0356.93016 |

[12] | Sandell, N. R.; Varaiya, P.; Athans, M.; Safonov, M. G., Survey of decentralized control methods for large scale systems, IEEE Trans Aut. Control, AC-23, 108 (1978) · Zbl 0385.93001 |

[13] | Sezer, M. E.; Hüseyin, O., Stabilization of linear interconnected systems using local state feedback, IEEE Trans Systems, Man, and Cybern., SMC-8, 751 (1978) · Zbl 0393.93035 |

[14] | Sezer, M. E.; Šiljak, D. D., On decentralized stabilization and structure of linear large-scale systems, Automatica, 17, 641 (1981) · Zbl 0464.93062 |

[15] | Šiljak, D. D., (Large-Scale Dynamic Systems: Stability and Structure (1978), North-Holland: North-Holland New York) · Zbl 0384.93002 |

[16] | Šiljak, D. D., Reliable control using multiple control systems, Int. J. Control, 31, 303 (1980) · Zbl 0428.93033 |

[17] | Šiljak, D. D.; Vukčević, M. B., Decentrally stabilizable linear and bilinear large-scale systems, Int. J. Control, 26, 289 (1977) · Zbl 0396.93031 |

[18] | Singh, M. G., (Decentralised Control (1981), North-Holland: North-Holland New York) |

[19] | Wang, S. H.; Davison, E. J., On the stabilization of decentralized control systems, IEEE Trans Aut. Control, AC-18, 473 (1973) · Zbl 0347.93030 |

[20] | Yasuda, K.; Hirai, K., Optimization of large-scale systems by means of decentralized state feedback, (14th Asilomar Conference Record (1980)), 516-520 |

[21] | Yasuda, K.; Hikata, T.; Hirai, K., On decentrally optimizable interconnected systems, (Proc. 19th IEEE Conference on Decision and Control (1980)), 536-537 |

[22] | Zukhovitskiy, S. I.; Ardeyeva, L. I., (Linear and Covex Programming (1966), Saunders: Saunders Philadelphia) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.