Stability, ℒ2L₂‐Gain, and ℋ∞H∞ Control of Linear Markov Jump Systems With Periodic Event‐Triggered Sampling in State and Mode

This article addresses the problems of stability, ‐gain analysis, and periodic event‐triggered control of linear stochastic Markov jump systems with sampled measurements in both state and mode. An impulsive system framework is developed for designing dynamic periodic event‐triggering mechanisms, modeling, and analyzing the closed‐loop system with asynchronous control induced by mode sampling. A second‐order moment equation of the stochastic Markov jump system is first established to derive non‐conservative stability criteria for the time‐triggered case. Subsequently, mode‐dependent periodic polynomial/discretized Lyapunov functions are constructed to establish sufficient criteria for ‐gain properties and mean‐square exponential stability of the event‐triggered case. The co‐design of the controller and event‐triggering function is accomplished using linear matrix inequalities. Comparative numerical examples validate the theoretical results.