Explicit formulas for LMI-based \(H_2\) filtering and deconvolution (Q5947654)

The paper studies an estimation method for a linear combination of the state and of the input of a time-invariant discrete-time linear system. The proposed technique is based on the solution of a set of linear matrix inequalities (LMI). Explicit formulas are provided for a suitable family of solutions to the LMI, and it is shown that a suboptimal estimator (in the sense of \(H_2\) performance) can be derived using such solutions.