Exponential input-to-state stability of non-linear reaction–diffusion systems with Markovian switching

Mean square exponential input-to-state stability (MSEISS) is studied for Markovian reaction–diffusion systems (MRDSs) with partial unknown transition probabilities. Firstly, the representation of the weak infinitesimal operator is derived for the partial differential system with Markovian switching. When transition probabilities are partially unknown, with the Lyapunov functional method, free constants and Wirtinger-type inequality, a sufficient condition is established to obtain the MSEISS for MRDSs where both the boundary input and in-domain input are considered. Then, the boundary controller is considered for MRDSs, and a sufficient criterion related to control gain is established to ensure the MSEISS and the effectiveness of controller is illustrated. In addition, the robust MSEISS is investigated for uncertain MRDSs. Finally, the derived results are illustrated via battery temperature management systems.