Simultaneous stabilization for uncertain descriptor systems with input saturation.

*(English)*Zbl 1263.93005Summary: The simultaneous stabilization problem for r uncertain descriptor systems is investigated. First, r uncertain closed-loop descriptor systems with an input saturation controller are introduced and a sufficient condition for these systems to be simultaneously stabilized is derived by a common generalized Lyapunov function. Meanwhile, an input saturation controller for these uncertain descriptor systems is designed via using linear matrix inequalities. Second, a simultaneous stability region for the r uncertain stabilized descriptor systems is investigated and described via system parameters. Furthermore, for the r different uncertain descriptor systems, the r different generalized Lyapunov functions are used to discuss the simultaneous stabilization problem with the advantage of relatively small conservativeness compared with the common generalized Lyapunov function. Of course, the advantages of the proposed method still include the numerical reliability of algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.

##### MSC:

93A14 | Decentralized systems |

93D30 | Lyapunov and storage functions |

93C10 | Nonlinear systems in control theory |

##### Keywords:

input saturation; lmis; simultaneous stabilization; stability region; generalized Lyapunov function
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\textit{Y. Chen} et al., Int. J. Robust Nonlinear Control 22, No. 17, 1938--1951 (2012; Zbl 1263.93005)

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