Stability of planar linear systems with state constraints

In this paper, a linear state-feedback controller design approach is proposed for linear time-invariant (LTI) planar systems with state constraints. Firstly, necessary and sufficient condition for stability of LTI constrained systems is presented by using null clines theorems. In addition, a method of designing stabilizing controller for LTI systems with state constraints is presented. Two examples are given to illustrate the efficiency of the design method.