Fixed-order robust filtering for linear uncertain systems (Q1354866)

The authors consider the robust \(H^\infty\) filtering problem for linear uncertain systems with components taking values in \(\mathbb{R}^n\) for different \(n\geq 1\). The \(H^\infty\)-type assumption means some standard restriction on matrices that connect the state, uncertainty input, disturbance input and measured output. The filter that is used is nonlinear time-varying and has a fixed order \(k\). The main result of the paper shows that for the fixed-order robust \(H^\infty\) filtering problem under consideration, there is no advantage to be obtained by using a nonlinear as opposed to a linear filter.