Finite‐Time Sliding Mode Control for IT2 Fuzzy Nonhomogeneous Markovian Switched Systems: An Asynchronous Observer‐Based Approach

ABSTRACT The asynchronous sliding‐mode control (SMC) issue for interval type‐2 (IT2) fuzzy Markovian switched systems with time‐varying delays is investigated in this paper. The Markovian chain is supposed to be nonhomogeneous. The finite‐time SMC problem is studied by constructing an asynchronous state observer via the hidden‐Markov model as a first attempt, which considers the situation that the system modes cannot be detected. Within a finite‐time interval, the system trajectories can be forced onto the constructed integral sliding surface in terms of the designed asynchronous controller. The finite‐time boundedness is analyzed both in the reaching and sliding phases. The asynchronous observer and controller gains are calculated via the linear matrix inequalities method. Two examples are provided to demonstrate the effectiveness and superiority of this approach.