[en] Many systems like servo systems, satellites, harddisks, and CD players, can be modeled as linear systems with a single integrator and a saturation. Many times, such systems are controlled with a PI controller resulting in a feedback interconnection with a double integrator and a saturation. In this paper, we propose a loop transformation that results in bounded operators so that classical analysis tools like muô€€€-analysis or IQCs can be applied. In order to show boundedness of all operators, we use quadratic surface Lyapunov functions to efficiently check if a double integrator in feedback with a saturation nonlinearity has L2 ô€€€-gain less than gamma > 0 ô€€€. We show that for many of such systems, the L2 ô€€€-gain is non-conservative in the sense that this is approximately equal to the lower bound obtained by replacing the saturation with a constant gain of .
[University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
