Positive stabilization and synchronization of Persidskii systems with hidden semi‐Markov process

Abstract This paper investigates the positive stochastic stabilization of the Persidskii systems with hidden semi‐Markov processes under partially known emission probabilities and the positive synchronization of a family of Persidskii systems. First, a hidden stochastic copositive Lyapunov function is introduced for the positive stochastic stabilization of systems. Accordingly, a criterion on positive stochastic stability is proposed for Persidskii systems with a hidden semi‐Markov process. Then, an observed mode‐dependent combining controller consisting of linear and nonlinear parts is designed in terms of matrix decomposition technique. Linear programming is employed to describe the presented conditions and compute the corresponding controller parameters. Finally, one example is provided to verify the effectiveness of the obtained results.