Global Stabilization of Planar Systems with Input Delay and Saturation

This chapter investigates the problem of global stabilization of planar linear systems with both actuator saturation and delay. For a double integrator system, two families of TPF-based linear feedback solutions to the problem are proposed. Both of these families of solutions are parameterized in a single-parameter γ. The first solution is delay dependent in the sense that the delay information is explicitly used in the controller design, while the second solution is delay independent as the delay information is not directly used in the feedback. For an oscillator system, we also propose a delay-dependent TPF-based controller. Explicit ranges of the value of γ for all the three cases are provided to guarantee the global stability of the closed-loop system.