Finite-Time Observer-Based Sliding Mode Control for Quantized Semi-Markov Switching Systems With Application

This article investigates the problem of sliding mode control (SMC) for semi-Markov switching systems (S-MSSs) with quantized measurement in finite-time level. The transition between different subsystems obeys a stochastic semi-Markov process related to nonexponential distribution. Additionally, due to the sensor information constraints, the state vectors are not always measurable in practice. Moreover, compared with existing results in literature, the output quantization is first considered for finite-time SMC problem via a logarithmic quantizer. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance onto the overall performance of the system under consideration. First, by the key points of stochastic semi-Markov Lyapunov function and observer design theory, a desired SMC law is constructed to guarantee that the system trajectories can arrive at the specified sliding surface (SSS) within an assigned finite-time level. Then, ST-dependent sufficient conditions are established to ensure the required finite-time boundedness performance including both reaching phase and sliding motion phase. Finally, the applicability of the proposed results is demonstrated by a single-link robot arm model.