l2 Performance Synthesis via Polynomial Parameter-Dependent Switching State Feedback Control for Constrained Systems

This paper proposes a switching control method based on error systems from multi-equilibrium points of constrained systems using homogeneous polynomial parameter-dependent saturating state feedback gains. First, mufti-equilibrium points are calculated from the origin to a steady state in state space regions. Next, analysis and synthesis conditions of the domain of lscr₂ performance for the systems can be recast as parameter-dependent matrix inequality conditions via the polytopic approach for the saturation. In particular, the parameter-dependent conditions are reduced to necessary and sufficient parameter-independent matrix inequality conditions based on Polya´s theorem. Hence, the state feedback gains are designed by derived synthesis linear matrix inequality conditions using off-line computation, and the gains are applied to the system by on-line computation of a proposed switching algorithm. Finally, it is confirmed through a numerical example that the proposed switching control is definitely helpful.