Adaptive feedback control for linear singular systems

An adaptive state feedback control approach for linear descriptor (or singular) systems is investigated in this paper, which makes the closed-loop dynamics of this class of systems regular, impulse-free, and stable. The proposed adaptive method is based on the Lyapunov theorem to ensure the admissibility of the descriptor system and it also provides the state tracking with the desired reference trajectory. First, a control law is generated to stabilize the equilibrium point of origin, and, after that, the method is extended to a state tracking controller. The presented controller not only gets the stable output tracking asymptotically but is also fairly simple compared to the existing methods in the literature proposed for the control problem of descriptor systems. Simulation results on controlling a sample descriptor system are presented to demonstrate the effectiveness of the proposed approach in this paper.