Quantized Fuzzy Finite-Time Control for Nonlinear Semi-Markov Switching Systems

Abstract

This brief considers quantized control for finite-time synthesis of nonlinear semi-Markov switching systems (S-MSSs) via T-S fuzzy strategy. The stochastic phenomena of structural and parametric changes are modeled by the semi-Markov process, in which the sojourn-time (ST) is deemed to obey a non-exponential distribution. Compared with previous works, the input quantization is firstly investigated for studying the finite-time control via a logarithmic quantizer. A key issue under the consideration is how to design a fuzzy-model-based finite-time control law in the presence of quantized error. For this purpose, by using the key point of Lyapunov function, the finite-time boundedness (FTBs) performance is analyzed via establishing sojourn-time-dependent sufficient conditions within a given finite-time level. Then, the existence of a quantized controller is given in standard LMIs. Finally, an example for an electric circuit shows the effectiveness of the finite-time control scheme.