SMC for Stirred Tank Reactor Model: Hybrid Systems With Bi-Boundary Sojourn Time

This work investigates sliding mode control (SMC) for stirred tank reactor (STR) under semi-Markov switching with bi-boundary sojourn time (ST). Compared with traditional discrete hybrid systems, both the upper and lower bounds of the ST are considered for each mode, providing a more accurate characterization of the system than the upper bound. Based on the statistical properties of the semi-Markov kernel (SMK), the SMK is assumed to be partly known. Owing to the limited research on SMC for discrete hybrid systems with semi-Markov switching and bi-boundary ST, the main contribution of this work is the development of the SMC law that guarantees the reachability of the quasi-sliding mode (QSM), together with a linear matrix inequality-based framework that accommodates partly known SMK information. The proposed SMC law drives the system states to a prespecified sliding region while effectively compensating for parameter uncertainties. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed control method.