A new stability test method for linguistic fuzzy state space models is proposed in this paper. This method allows the determination of stability of fuzzy models by applying the Lyapunov function to each rule. A gradient-based algorithm is suggested to simplify the stability tests. Using this algorithm, the Lyapunov equation can be updated towards the direction where the stability can be determined more correctly. An additional gradient-based stabilizing algorithm is also derived, which allows a systematic approach to find stabilizing controls by updating the Lyapunov equations towards the direction where unstable eigenvalues are decreased. Examples demonstrate the convenience of the stability test and the two suggested gradient-based algorithms.