Recursive state estimation for two-dimensional shift-varying systems with random parameter perturbation and dynamical bias

Abstract In this paper, the state estimation problem is investigated for a class of two-dimensional (2-D) stochastic systems with shift-varying parameters. The stochasticity with the underlying system comes from three sources, namely, random parameter perturbations, dynamical biases and additive white noises. The measurement output is subject to the uniform quantization as a result of communication constraints on the sensors. The purpose of the addressed problem is to recursively estimate the system states with prescribed estimation performance in spite of the stochastic disturbances and the uniform quantizations. An augmented model is first constructed to combine the information about the state and the bias, and the dynamical evolution is subsequently discussed. Furthermore, through stochastic analysis and mathematical induction, the estimator design algorithm is developed to acquire certain upper bound on the estimation error variance and such an upper bound is then minimized in the matrix-trace sense. Moreover, the boundedness issue of the estimation errors is investigated via matrix inversion lemma and inductive analysis technique. Finally, the effectiveness of the proposed state estimation algorithm is validated on a typical 2-D system modeled by the well-known Darboux equation with extensive application potentials in industrial processes.