Relaxed local nonquadratic stabilization for nonhomogeneous hidden Markov jump fuzzy systems over non-closed system operating range

Abstract

This paper is dedicated to investigating the problem of relaxed local nonquadratic stabilization of nonhomogeneous hidden Markov jump fuzzy systems (HMJFSs) over a non-closed system operating range in the continuous-time domain. Within the framework of the mode-dependent nonquadratic Lyapunov function, the proposed method formulates the local stabilization conditions in a less conservative manner. Different from other recent studies, our formulation process is carried out without assumptions on the additional state restrictions required to establish a closed operating range, which opens the possibility to further increase the size of the domain of attraction. Furthermore, this method provides a systematic way to solve the nonconvex problem arising from the asynchronism between hidden and observed modes through augmented state-based congruent transformations. Not only that, significant progress is made in further reducing conventional conservatism and computational complexity by removing unnecessary auxiliary conditions. Finally, two numerical examples are given to show the validity of the proposed method.