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L2 stability, H control of switched homogeneous nonlinear systems and their semi-tensor product of matrices representation

Authors

  • Lijun Zhang,

    1. College of Automation, Harbin Engineering University, Harbin, China
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    • Lijun Zhang is now with the School of Marine Technology, Northwestern Polytechnical University, Xi'an, 710072, China.

  • Kuize Zhang

    Corresponding author
    • College of Automation, Harbin Engineering University, Harbin, China
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Correspondence to: Kuize Zhang, College of Automation, Harbin Engineering University, Harbin 150001, China.

E-mail: zkz0017@163.com

SUMMARY

This paper investigates the problems of L2 stability and H control of switched homogeneous nonlinear systems. This paper gives that if a switched homogeneous nonlinear system with disturbance is internally homogeneously asymptotically stable, then it has a finite L2 gain, and if a switched homogeneous nonlinear system with disturbance and controls is homogeneously stabilizable under the zero disturbance condition, its H control problem is solvable under some mild conditions, and a homogeneous solution is given. Then, via the semi-tensor product of matrices method, the aforementioned obtained results are transformed to linear-like forms, and the aforementioned obtained Hamilton–Jacobi–Isaacs inequality is transformed to a linear-like matrix inequality, which makes it feasible to compute the solutions by computer. Copyright © 2012 John Wiley & Sons, Ltd.

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