$${\cal{H}}_{\infty}$$ and $${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$$ Model Reduction for System Input with Sector Nonlinearities

J. Lam, H. Gao, S. Xu and C. Wang
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J. Lam: University of Hong Kong
H. Gao: Harbin Institute of Technology
S. Xu: Nanjing University of Science and Technology
C. Wang: Harbin Institute of Technology

Journal of Optimization Theory and Applications, 2005, vol. 125, issue 1, No 7, 137-155

Abstract: Abstract This paper investigates the problems of model reduction for linear continuous-time systems with input sector nonlinearities. Two objectives ( $${\cal{H}}_{\infty}$$ and $${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$$ ) are employed to evaluate the approximation performance and the problems are solved by using linear matrix inequality (LMI) techniques, with sufficient conditions obtained for the existence of desired reduced-order models. Since some matrix inequality constraints are involved in these conditions, the cone complementarity linearization idea is utilized to cast the nonconvex feasibility problem into a sequential minimization problem subject to LMI constraints. A numerical example is presented to show the effectiveness of the proposed theories.

Keywords: Cone complementarity linearization; model reduction; linear matrix inequalities; input sector nonlinearities (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-1714-6

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