This paper focuses on the stochastic stabilization of hidden semi-Markov jump nonlinear positive systems. First, a notion of stochastic stability is introduced for this class of systems. A criterion is addressed to ensure the stochastic stability using a stochastic copositive Lyapunov function. Then, an observed mode is proposed to estimate the emitted value of the hidden semi-Markov process and the mode-dependent controller is designed using an improved matrix decomposition approach. Some auxiliary variables are added to decouple the coupling terms in hidden semi-Markov jump nonlinear positive systems into a tractable condition. All conditions are described in terms of linear programming. Moreover, the proposed design is developed for systems with partially known emission probabilities. Two examples are provided to show the validity of the obtained results.

This paper considers the practical consensus of time-varying fuzzy positive multi-agent systems. A novel error variable is introduced by adding an additional constant term. Under the framework of time-varying fuzzy copositive Lyapunov functions, a fuzzy control protocol with time-varying gain matrices is designed in terms of matrix decomposition technique. Some consensus conditions are addressed via time-varying linear programming. Moreover, the design is developed for false data injection attacks. Finally, two examples are provided for verifying the validity of the design.