H _∞ and H ₂ optimal sampled-data controller synthesis: A hybrid systems approach with mixed discrete/continuous specifications

In this paper, a tractable sampled-data controller synthesis method is proposed for linear time-invariant plants that gives guarantees for stability and performance of the closed-loop system in terms of the H _∞- and H ₂-norm. This is done by taking a so-called jump/hybrid systems approach, which allows formulating linear matrix inequalities using an explicit solution to the Riccati differential equation. Furthermore, the sampled-data problem is formulated such that continuous-time design techniques like H _∞ loop-shaping can be used in a sampled-data context. To do so, it is essential to consider mixed discrete/continuous specifications, in which both discrete and continuous signals are weighted using weighting filters. This leads to a generalised plant that has both continuous-time and discrete-time dynamics. The controller design method is demonstrated on a benchmark example, in which we compare to existing results in the literature, and on a design example of reference tracking of a two-mass–spring–damper system.