GeneralizedH₂control of the linear system with semi‐Markov jumps

This article studies a class of asynchronous generalized H 2 control problems for continuous‐time discrete‐state semi‐Markov jump linear systems. By constructing a Lyapunov function based on the semi‐Markov process, introducing a weak infinitesimal operator and applying the smoothness of the expectation, sufficient conditions are obtained to ensure stochastic stability and generalized H 2 performance of the system. Simultaneously, equivalent conditions are given by introducing slack variables and an asynchronous controller is designed. Moreover, we derive the sufficient conditions for the case where the transition rate is partially unknown. Finally, we use the cone complement linearization iterative algorithm to simulate two examples to prove the effectiveness of the design scheme.