Robustly quadratic dissipative analysis and control for multivariable linear discrete-time systems

Robustly quadratic dissipative analysis and control for a class of uncertain multivariable linear discrete-time systems are considered. The uncertainties are expressed in a linear fractional form. By constructing augmented systems, the robustly quadratic dissipative analysis and control for the uncertain systems are converted into the quadratic dissipative analysis and design of the systems without uncertainties. Necessary and sufficient conditions for the uncertain systems to be robustly quadratic dissipative are derived and the solution of the robustly quadratic dissipative control is got using LMI approach. The results of the paper unify existing results on H_∞ control and positive real control and provide a more flexible and less conservative control design.