Research on Stabilization Algorithm of Linear Constrained System

The control problem of linear continuous-time systems with constraints of control, state and initial state is studied. State feedback control law of linear constrained system is designed based on positively invariant sets of linear system so that all given initial states of system transfer asymptotically to the origin while all constraints are satisfied. First, the problem of the existence of the linear state feedback control law is presented, the constrained control problem is converted to nonlinear optimization problem by positively invariant sets approach and optimization theory. Then, the nonlinear optimization problem is solved through random trying method and the state feedback control law of the linear constrained system is obtained. Finally, simulation results show that the control law obtained in this paper is effective.