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**Lyapunov-based switching control of nonlinear systems using high-gain observers.**
*(English)*
Zbl 1140.93456

Summary: We consider output feedback stabilization of uniformly observable uncertain nonlinear systems when the uncertain parameters belong to a known but comparably large compact set. In a previous paper, we proposed a new logic-based switching control to improve the performance of continuous high-gain-observer-based sliding mode controllers. Our main goal here is to show that similar techniques can be exploited for solving challenging control problems for a more general class of uncertain nonlinear systems. We require neither the sign of the high-frequency gain to be known nor the system to be minimum-phase. The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if, after a dwell-time period, the derivative of the Lyapunov function does not satisfy a certain inequality. A high-gain observer is used to estimate the derivatives of the output as well as the derivative of the Lyapunov function. Another goal of this paper is to introduce a switching strategy that uses on-line information to decide on the controller to switch to, instead of using a pre-sorted list as in our previous work. The new strategy can improve the transient performance of the system.

### MSC:

93D15 | Stabilization of systems by feedback |

93D30 | Lyapunov and storage functions |

93C10 | Nonlinear systems in control theory |

### Keywords:

switching control; Lyapunov design; high-gain observers; nonlinear uncertain systems; practical stabilization
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\textit{L. B. Freidovich} and \textit{H. K. Khalil}, Automatica 43, No. 1, 150--157 (2007; Zbl 1140.93456)

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### References:

[1] | Angeli, D.; Mosca, E., Lyapunov-based switching supervisory control of nonlinear uncertain systems, IEEE Transactions on Automatic Control, 47, 500-505 (2002) · Zbl 1364.93696 |

[2] | Corradini, M. L.; Orlando, G., A switching controller for the output feedback stabilization of unknown uncertain interval plants via sliding modes, IEEE Transactions on Automatic Control, 47, 2101-2107 (2002) · Zbl 1364.93627 |

[3] | Freidovich, L.B. (2005). Logic-based switching control of nonlinear systems using high-gain observers; Freidovich, L.B. (2005). Logic-based switching control of nonlinear systems using high-gain observers |

[4] | Freidovich, L. B.; Khalil, H. K., Logic-based switching for the robust control of minimum-phase nonlinear systems, Systems and Control Letters, 54, 713-727 (2005) · Zbl 1129.93412 |

[5] | Hespanha, J. P.; Liberzon, D.; Morse, A. S., Overcoming the limitations of adaptive control by means of logic-based switching, Systems and Control Letters, 49, 49-65 (2003) · Zbl 1157.93440 |

[6] | Khalil, H. K., Nonlinear systems (2002), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0626.34052 |

[7] | Liberzon, D., Switching in systems and control (2003), Birkhäuser: Birkhäuser Boston, MA · Zbl 1036.93001 |

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