Digital Redesign of Linear Time-Invariant Systems: Integral Quadratic Constraint Approach

In this paper, a new digital redesign (DR) technique with an integral quadratic constraint (IQC) is presented. The DR problem can be interpreted as finding a relevant digital gain to minimize the IQC, which describes the energy of error response between the continuous-time and the sampled-data closed-loop systems for all time. It can be shown that the IQC for all time is reduced to two conditions, where one is a state-matching condition at the sampling points and the other is the IQC for the sampling period. These constructive conditions are formulated in terms of the linear matrix inequalities (LMls). A numerical example is provided for visualizing the feasibility of the proposed technique