LMI-based design for regional fixed-time nonlinear control with settling time and control constraints

The problem of designing a nonlinear control such that the control magnitude and settling time of the closed-loop system regionally satisfy prescribed bounds is considered. Such a control is termed a regional, magnitude constrained, time constrained control. Using common Lyapunov functions, sufficient conditions are derived to solve the design problem and a control synthesis procedure involving a sequence of linear matrix inequalities is presented. The conditions and procedure are applied to three examples including single-input and two-input relative orbital motion control.