Two-Layer Asynchronous Control for a Class of Nonlinear Jump Systems: An Interval Segmentation Approach

Abstract

This article proposes the two-layer asynchronous control scheme for a class of networked nonlinear jump systems. For the constructed system in a network environment, the data transmission may suffer from many restrictions, such as incomplete acceptable mode information and transition information, nonlinearity of system and inadequate bandwidth resources, etc. Then, the two-layer asynchronous controller is developed to stabilize the plant constructed by Takagi-Sugeno (T-S) fuzzy method and semi-Markov theory (SMT). Herein, the hidden semi-Markov process with time-varying emission probability is introduced to establish the relation between the system modes and the controller modes, in which the interval segmentation method is presented to deal with this time-varying probability. Compared with some published results, this method can make full use of the transition rate information, which may lead to the reduction of conservatism in the proposed asynchronous control design. At the same time, the limited bandwidth problem in the communication channel is addressed by introducing the bilateral quantization strategy, and the new sufficient conditions are derived on the stochastic stability of the nonlinear jump system with/without incomplete transition and sojourn-time information. Finally, the numerical simulation examples about DC motor illustrate the effectiveness and the feasibility of the proposed approach.