Variance-Constrained State Estimation for Networked Multi-rate Systems with Measurement Quantization and Probabilistic Sensor Failures

This paper is concerned with the variance-constrained state estimation problem for a class of networked multi-rate systems (NMSs) with network-induced probabilistic sensor failures and measurement quantization. The stochastic characteristics of the sensor failures are governed by mutually independent random variables over the interval [0, 1]. By applying the lifting technique, an augmented system model is established to facilitate the state estimation of the underlying NMSs. With the aid of the stochastic analysis approach, sufficient conditions are derived under which the exponential mean-square stability of the augmented system is guaranteed, the prescribed H∞ performance constraint is achieved and the individual variance constraint on the steady-state estimation error is satisfied. Based on the derived conditions, the addressed variance-constrained state estimation problem of NMSs is recast as a convex optimization one that can be solved via the semi-definite program method. Furthermore, the explicit expression of the desired estimator gains is obtained by means of the feasibility of certain matrix inequalities. Two additional optimization problems are considered with respect to the H∞ performance index and the weighted error variances. Finally, a simulation example is utilized to illustrate the effectiveness of the proposed state estimation method. Index Terms Networked multi-rate systems; Variance constraint; H∞ state estimation; Measurement quantization; Probabilistic sensor failures.