Nonlinear Dynamics

, Volume 77, Issue 3, pp 1011–1017 | Cite as

Robust \({\varvec{L}}_{\varvec{2}}\)-gain control for a class of cascade switched nonlinear systems

  • Yue Liu
  • Shengzhi Zhao
  • Ruicheng Ma
Original Paper


In this paper, we study the robust finite \(L_2 \)-gain control for a class of cascade switched nonlinear systems with parameter uncertainty. Each subsystem of the switched system under consideration is composed of a zero-input asymptotically stable nonlinear part which is a lower dimension switched system, and of a linearizable part. The uncertainty appears in the control channel of each subsystem. We give sufficient conditions under which the nonlinear feedback controllers are derived to guarantee that the \(L_2 \)-gain of the closed-loop switched system is less than a prespecified value for all admissible uncertainty under arbitrary switching. Moreover, we also develop the \(L_2\)-gain controllers for the switched systems with nonminimum phase case.


Switched nonlinear system Parameter uncertainty Common Lyapunov function \(L_2\)-gain 



This work was supported by A Project Supported by Scientific Research Fund of Liaoning Provincial Education Department under Grant L2013002 and the National Natural Science Foundation of China under Grant 61304055.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of MathematicsLiaoning UniversityShenyangPeople’s Republic of China

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