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\(L_{2}\)-gain analysis and control of saturated switched systems with a dwell time constraint

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Abstract

This paper investigates the \(L_{2}\)-gain analysis and control problem for switched systems with actuator saturation. A minimal dwell time constraint is first introduced, which avoids possible arbitrarily fast switching. Then, to satisfy the mentioned constraint, a switching strategy depending only on a lower bound of the dwell time and partial measurable states of the closed-loop system is developed in output feedback framework, which extends previous results in state feedback framework. Further, under the proposed switching strategy, time-varying hull controllable regions and saturated output feedback controllers working on them are constructed such that the closed-loop system has a prescribed \(L_{2}\)-gain. Meanwhile, the states of the system starting from the origin will remain inside a time-varying ellipsoid determined by a discretized Lyapunov matrix function. In addition, the resulting ellipsoid is also proven to be between two time-invariant ellipsoids. A solution of the considered problem is given via a linear matrix inequality formulation. Finally, an example is exploited to illustrate the effectiveness of the theoretical results.

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Acknowledgments

This work was supported in part by the Funds of National Science of China (Grant no. 61273148, 61420106016), the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (Grant no. 201157), and the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries (Grant no. 2013ZCX01).

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China

    Guang-Xin Zhong

  2. State Key Laboratory of Synthetical Automation of Process Industries, College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China

    Guang-Hong Yang

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  1. Guang-Xin Zhong
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  2. Guang-Hong Yang
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Correspondence to Guang-Hong Yang.

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Zhong, GX., Yang, GH. \(L_{2}\)-gain analysis and control of saturated switched systems with a dwell time constraint. Nonlinear Dyn 80, 1231–1244 (2015). https://doi.org/10.1007/s11071-015-1939-y

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