Robust \({\mathcal H}_\infty\)-filtering design with pole placement constraint via linear matrix inequalities (Q1807814)

Consider the linear time-invariant continuous system \(x'(t)= Ax(t)+ Bw(t)\), \(x(0)= x_0\) with state vector \(x(t)\), measurements output vector \(y(t)= Cx(t)+ Dw(t)\), noise signal vector \(w(t)\) and estimated signal \(z(t)= Lx(t)+ Tw(t)\). Here the matrix 6-tuple \((A,B,C,D,L,T)\) is uncertain and belongs to a given convex compact set of polytopic type. A robust filter is designed for which the filtering error is quadratically stable. Conditions for existence of the robust filter are given in terms of linear matrix inequalities (LMI) which can be solved by standard optimization techniques. A filter synthesis procedure under pole placement conditions is also considered. The latter requires the solution of additional LMI's.