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

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.