Robust quadratic dissipative analysis and control for (discrete-time) systems

The robust quadratic dissipative control problem for a class of uncertain discrete-time systems is (considered) where the uncertainties are expressed in a linear fractional form. Equivalence between quadratic (dissipativeness) and positive realness is established, and necessary and sufficient (conditions) are derived for (linear) systems to be strict quadratic dissipative. It is shown that the quadratic dissipative analysis and control of the (uncertain) systems can be reduced to those of related systems without uncertainties. Necessary and sufficient (conditions) are obtained for the uncertain systems to be robust quadratic dissipative. The robust quadratic dissipative control problem can be solved using an LMI (approach.) An example shows the applicability of the proposed (approach.)