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Stabilisation and H∞ control of a class of non-linear Hamiltonian descriptor systems with application to non-linear descriptor systems

Stabilisation and H∞ control of a class of non-linear Hamiltonian descriptor systems with application to non-linear descriptor systems

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  • Author(s): L.Y. Sun 1, 2  and  Y.Z. Wang 2
    • View affiliations
    • Affiliations: 1: School of Science, University of Jinan, Jinan, People's Republic of China
      2: School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China
  • Source: Volume 4, Issue 1, January 2010, p. 16 – 26
    DOI:  10.1049/iet-cta.2008.0324 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

This study investigates the stabilisation and H∞ control of a class of non-linear Hamiltonian descriptor systems (NHDSs) with application to non-linear descriptor systems (NDSs). Based on the structural characteristic of the NHDS, an equivalent non-linear Hamiltonian differential-algebraic system is obtained, and then the equivalent system is transformed into a strictly dissipative Hamiltonian form by a suitable state feedback. With the dissipative form, a stabilisation control law is developed, based on which an H∞ controller is designed for the NHDSs with external disturbances. Finally, the obtained results for the Hamiltonian descriptor system are applied to NDSs, and a sufficient condition under which the systems can be transformed into a strictly dissipative Hamiltonian form is given. Simulation results show the efficiency of the controllers proposed in this study.

Inspec keywords: nonlinear control systems; state feedback; stability; differential algebraic equations; H∞ control

Other keywords: nonlinear Hamiltonian differential-algebraic system; state feedback; nonlinear Hamiltonian descriptor system; H∞ control; nonlinear descriptor system; stabilisation control; dissipative Hamiltonian form

Subjects: Stability in control theory; Nonlinear control systems; Algebra; Optimal control

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