Multi-objected optimal control problem for singularly perturbed systems based on passivity

In this paper, the multi-objected optimal control problem for singularly perturbed systems based on passivity is considered. First, the problem of the asymptotically stability under passive performance constraint is studied in terms of Lyapunov stability theory. Second, a sufficient condition for the existence state feedback controller is presented, so that the resulting closed-loop system is asymptotically stable and passive. Furthermore, in light of the passive controller, the linear quadratic optimal control problem is constructed, in which the weight matrices of the performance index can be calculated. Finally, two numerical examples are provided to demonstrate the effectiveness and correctness of the proposed results.