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A scheme for globally stabilized controller design was proposed based on stability criterion of density function and solved via SOS (sum of squares) decomposition tool. In order to deduce the complexity of the controller, it was designed with minimum monomial terms which approximated by minimizing the norm 1 coefficients of controller monomials. Guaranteed convergence rate performance was considered for locally stabilized controller, and finally, a switching control switched between global and local controllers was addressed to enhance system performance. The proposed control scheme achieved effective performance as illustrated in numerical example.