TY - JOUR
T1 - Composite fuzzy control of nonlinear singularly perturbed systems
AU - Li, Tzuu Hseng S.
AU - Lin, Kuo Jung
N1 - Funding Information:
Manuscript received February 24, 2004; revised June 18, 2005 and September 19, 2005. This work was supported by the National Science Council, Taiwan, the Republic of China, by Grants NSC93-2213-E006-033 and NSC93-2213-E006-129.
PY - 2007/4
Y1 - 2007/4
N2 - This paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed (NSP) systems with guaranteed H∞ control performance. We use the Takagi-Sugeno (T-S) fuzzy model to construct the singularly perturbed fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. At first, a set of common positive-define matrices and the controller gains are determined by the Lyapunov stability theorem and linear matrix inequality (LMI) approach. Then, a sufficient condition is derived for the robust stabilization of NSP systems. The composite fuzzy control will stabilize the original NSP systems for all ε ε (0, ε*) and the allowable perturbation bound ε* can be determined via some algebra inequalities. A practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme.
AB - This paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed (NSP) systems with guaranteed H∞ control performance. We use the Takagi-Sugeno (T-S) fuzzy model to construct the singularly perturbed fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. At first, a set of common positive-define matrices and the controller gains are determined by the Lyapunov stability theorem and linear matrix inequality (LMI) approach. Then, a sufficient condition is derived for the robust stabilization of NSP systems. The composite fuzzy control will stabilize the original NSP systems for all ε ε (0, ε*) and the allowable perturbation bound ε* can be determined via some algebra inequalities. A practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme.
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U2 - 10.1109/TFUZZ.2006.878252
DO - 10.1109/TFUZZ.2006.878252
M3 - Article
AN - SCOPUS:34147132661
SN - 1063-6706
VL - 15
SP - 176
EP - 187
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
IS - 2
ER -