Uncertainty Modeling and Robust Control of LTI Systems Based on Integral Quadratic Constraints

Based on experimental data a joint method for nominal model error modeling and robust control is presented for linear time-invariant (LTI) systems. The goal of the method is to design a controller that attain robust quadratic performance and stability of the closed loop, and simultaneously construct an uncertainty model that is not invalidated by measurement data. The problem is motivated by the need for non-conservative and reliable modeling of neglected or unknown dynamics and effect of outer disturbances. The components of dynamic errors and disturbances are balanced in the model in order to improve conditions for designing the specified controller. The problem statement and solution is formulated in terms of integral quadratic constraints (IQCs) and linear matrix inequalities (LMIs). The resulted method is a modified version of the well-known DK-iteration in
μ
-synthesis.