Stability Analysis of Regular and Sliding Motions of Linear Dynamical Systems with Ideal Relay

The preference given to relay control systems has practical as well as theoretical aspects because of their simplicity, their low costs and their (sub-) optimality. The analysis and synthesis of relay control systems has to investigate the particular phenomenon of sliding motions along switching surfaces. Here, the stability behavior of regular and sliding motions of linear dynamical systems containing ideal relays is analyzed assuming linear switching functions.