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LMI relaxations for nonlinear fuzzy control systems via homogeneous polynomials

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2 Author(s)
Jia-Ren Wan ; Dept of Mech. Eng., Nat. Central Univ., Jhongli ; Ji-Chang Lo

Based on recent results on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) that arise from robust stability of linear parameter varying (LPV) systems, we investigate the relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of firing strength belonging to the unit simplex, exploiting the algebraic property of Polyapsilas theorem to construct a family of finite-dimensional LMI relaxations. The main contribution of this paper is that sets of relaxed LMIs are parameterized in term of the polynomial degree d. As d increases, progressively less conservative LMI conditions are generated, being easier satisfied due to more freedom provided by new variables involved. An example to illustrate the relaxation is provided.

Published in:

Fuzzy Systems, 2008. FUZZ-IEEE 2008. (IEEE World Congress on Computational Intelligence). IEEE International Conference on

Date of Conference:

1-6 June 2008