On constructing constrained control Lyapunov functions for linear systems

This works considers control of linear systems with input constraints and presents a constructive procedure for constrained control Lyapunov functions (CCLFs). First, the definition of a CLF is generalized to formulate the requirements of a CCLF and then a CCLF construction procedure is presented that can be utilized within Lyapunov-based control designs to stabilize the system from all initial conditions in the null-controllable region (the set of initial conditions from where the system can be stabilized subject to input constraints).