Robust stability analysis for discrete-time LQG system under finite wordlength effects, noise uncertainties and time-varying structured parameter perturbations

In this paper, a sufficient condition is proposed to analyze the robust stability of the discrete-time LQG system under linear time-varying structured parameter perturbations, noise uncertainties and finite wordlength effects. Digital controllers are realized with floating-point arithmetic. The robust stability condition presented in this paper can be used to analyze the stability of the discrete-time LQG systems with a linear time-varying perturbation matrix due to the combination of structured parameter perturbations, feedback gain quantization error, estimator gain quantization error and computational roundoff errors. An example is given to illustrate the application of the proposed robust stability criterion.