Robust analysis of sampled data controllers (Linear matrix inequalities)

Uncertainties in a plant's dynamics and in its input and output channels make it difficult for a control system to obtain good performance characteristics and stability of the closed-loop system. These difficulties arise both in continuous-time and discrete-time, but are exemplified in the sampled-data control problem. In the present work, the effects of uncertainties on the robust stability and performance of continuous-time, discrete-time and sampled-data systems is quantified using an H₂ performance measure.; For continuous-time and discrete-time systems, robust stability and performance bounds are formulated in terms of guaranteed cost inequalities. New guaranteed cost bounds are derived for plants with real structured uncertainty and are given in their equivalent LMI form. For continuous-time systems, a shifted linear bound and a shifted inverse bound are obtained. LMI forms are given for these bounds and for the shifted bounded real bound and shifted Popov bound. For discrete-time systems, a linear bound, an inverse bound, a shifted bounded-real bound, and a shifted Popov bound are obtained. LMI forms are given for these bounds. For both systems, comparisons are made between the shifted bounds, their unshifted counterparts and bounds based on standard LMI techniques.; Finally, the sampled-data robust stability and performance problem is considered. The closed-loop performance of a sampled-data control system under plant uncertainty is investigated by utilizing exact discretization techniques. In particular, for an H₂ performance measure, exact expressions for the closed-loop, state, cross-weighting, and control costs are obtained for a given sample interval h. LMI techniques are used to bound the worst-case performance given input and output uncertainties, and additional consideration is given to the case in which controllability is lost due to sampling. After applying discrete-time LQG synthesis to the sampled-data system, the achievable performance is evaluated for fast sampling h → 0 and for slow sampling h → ∞.