Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness
SIAM Journal on Matrix Analysis and Applications
Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi-Sugeno's form
International Journal of Systems Science
Stabilization of Takagi-Sugeno model via nonparallel distributed compensation law
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
An approach to fuzzy control of nonlinear systems: stability and design issues
IEEE Transactions on Fuzzy Systems
Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs
IEEE Transactions on Fuzzy Systems
Piecewise quadratic stability of fuzzy systems
IEEE Transactions on Fuzzy Systems
New approaches to relaxed quadratic stability condition of fuzzy control systems
IEEE Transactions on Fuzzy Systems
A multiple Lyapunov function approach to stabilization of fuzzy control systems
IEEE Transactions on Fuzzy Systems
Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems
IEEE Transactions on Fuzzy Systems
Automatica (Journal of IFAC)
New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI
Automatica (Journal of IFAC)
Information Sciences: an International Journal
Information Sciences: an International Journal
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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 commonquadratic 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 parameterdependent 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.