Time and Frequency domain design of Functional Filters

Abstract-This paper proposes both time and frequency domain design of functional filters for linear time-invariant multivariable systems where all measurements are affected by disturbances. The order of this filter is equal to the dimension of the vector to be estimated. The time procedure design is based on the unbiasedness of the filter using a Sylvester equation; then the problem is expressed in a singular system one and is solved via Linear Matrix Inequalities (LMI) to find the optimal gain implemented in the observer design. The frequency procedure design is derived from time domain results by defining some useful Matrix Fractions Descriptions (MFDs) and mainly, establishing the useful and equivalent form of the connecting relationship that parameterizes the dynamic behavior between time and frequency domain, given by Hippe in the reduced-order case. A numerical example is given to illustrate our approach

Distributed information consensus filters for simultaneous input and state estimation

This paper describes the distributed information filtering where a set of sensor networks are required to simultaneously estimate input and state of a linear discrete-time system from collaborative manner. Our research purpose is to develop a consensus strategy in which sensor nodes communicate within the network through a sequence of Kalman iterations and data diffusion. A novel recursive information filtering is proposed by integrating input estimation error into measurement data and weighted information matrices. On the fusing process, local system state filtering transmits estimation information using the consensus averaging algorithm, which penalizes the disagreement in a dynamic manner. A simulation example is provided to compare the performance of the distributed information filtering with optimal Gillijins–De Moor’s algorithm

Complements to full order observer design for linear systems with unknown inputs

This note completes the obtained results in [1]. It presents a full-order observers for linear systems with unknown inputs in the state and in the measurement equations. It gives a more general approach for the observers design than that presented in [1] and it shows that all the obtained results are independent of the choice of the generalized inverses considered in the observers design. Continuous and discrete time systems are considered