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Homogeneous Polynomially Nonquadratic Stabilization of Discrete-Time Takagi–Sugeno Systems via Nonparallel Distributed Compensation Law

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1 Author(s)
Baocang Ding ; Coll. of Autom., Chongqing Univ., Chongqing, China

This paper considers stability of discrete-time nonlinear systems in Takagi-Sugeno (T-S) form. This problem has been studied for more than 20 years with many sufficient conditions, and the asymptotically necessary and sufficient (ANS) conditions with respect to the common-quadratic Lyapunov, function, having being obtained. This paper considers general forms of homogeneous polynomially nonquadratic Lyapunov (HPNQL) function and homogeneous polynomially parameterized nonparallel distributed compensation (HPP-non-PDC) law. By generalization of the procedure based on Pólya's theorem and techniques used for parameter-dependent linear matrix inequality (PD-LMI) which have been studied previously in different contexts, ANS stability conditions with respect to the general HPNQL function are obtained.

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Fuzzy Systems, IEEE Transactions on  (Volume:18 ,  Issue: 5 )