Deadbeat Input Reconstruction and State Estimation for Discrete-Time Linear Time-Varying Systems

The objective of input reconstruction is to use knowledge of the output of a system to estimate the input. An estimate of the input can be used in an observer to provide more accurate state estimates. This paper presents a technique for combined state and input estimation for discrete-time, linear time-varying systems. The algorithm is based on the analysis of the rank of the time-dependent matrix that relates vectors of states and input values to a vector of outputs. The key contribution is a characterization of the time-varying delay under which the state and input can be estimated. The input and state estimate are given in terms of the generalized inverse of a partitioned matrix. The approach is demonstrated on discrete-time examples with linear periodically time-varying dynamics.