Mixed H2/H∞ control for time-varying and linear parametrically-varying systems
Carsten W. Scherer · International Journal of Robust and Nonlinear Control · 1996
This paper provides a solution of the mixed H2/H∞ problem with reduced order controller for time-varying systems in terms of solvability of differential linear matrix inequalities and rank conditions, including a detailed discussion of how to construct a controller. Immediate specialization leads to a solution of the full order problem and the mixed H2/H∞ problem for linear systems whose description depends on an unknown but, in real-time, measurable time-varying parameter. As known for the H∞ problem, we completely resolve the quadratic mixed H2/H∞ problem (under certain hypotheses on the parameter dependence) by reducing it to the solution of finitely many algebraic linear matrix inequalities. However, we also point out directions of how to overcome the conservatism introduced by using constant solutions of the differential inequalities. Finally, we clarify that a simple specialization leads to a linear matrix inequality approach to the pure H2 problem for general LTI systems, and we reveal how to compute the optimal value.