TY - JOUR
T1 - Stabilization of singularly perturbed fuzzy systems
AU - Li, Tzuu Hseng S.
AU - Lin, Kuo Jung
N1 - Funding Information:
Manuscript received August 26, 2002; revised April 28, 2003 and November 26, 2003. This work was supported by the National Science Council of the Republic of China under Grants NSC91-2213-E006-026 and NSC92-2213-E006-071. The authors are with IC S Laboratory, Department of Electrical Engineering, National Cheng-Kung University, Tainan, Taiwan 701, R.O.C. Digital Object Identifier 10.1109/TFUZZ.2004.834822
PY - 2004/10
Y1 - 2004/10
N2 - This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the first design method, we propose the composite fuzzy control to stabilize the SPF subsystem with H∞ control performance. Based on the Lyapunov stability theorem, the stability conditions are reduced to the linear matrix inequality (LMI) problem. The composite fuzzy control will stabilize the original SP nonlinear systems for all ε ∈ (0, ε*) and the upper bound ε* can be determined. For the second design method, we present a direct fuzzy control scheme to stabilize the SP nonlinear system with H∞ control performance. By utilizing the Lyapunov stability theorem, the direct fuzzy control can guarantee the stability of the original SP nonlinear systems for a given interval ε € [ε, ε]. The stability conditions are also expressed in the LMIs. Two SP nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes.
AB - This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the first design method, we propose the composite fuzzy control to stabilize the SPF subsystem with H∞ control performance. Based on the Lyapunov stability theorem, the stability conditions are reduced to the linear matrix inequality (LMI) problem. The composite fuzzy control will stabilize the original SP nonlinear systems for all ε ∈ (0, ε*) and the upper bound ε* can be determined. For the second design method, we present a direct fuzzy control scheme to stabilize the SP nonlinear system with H∞ control performance. By utilizing the Lyapunov stability theorem, the direct fuzzy control can guarantee the stability of the original SP nonlinear systems for a given interval ε € [ε, ε]. The stability conditions are also expressed in the LMIs. Two SP nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes.
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U2 - 10.1109/TFUZZ.2004.834822
DO - 10.1109/TFUZZ.2004.834822
M3 - Article
AN - SCOPUS:7244252928
SN - 1063-6706
VL - 12
SP - 579
EP - 595
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
IS - 5
ER -