With Constraints Of The Generalized System Of Regulation Problem

The constrained solutions to the nonlinear matrix equation XA+XBX=HX and the regulation problems for descriptor linear systems with constrained states and controls are investigated in this thesis.Firstly, the constrained solutions to the nonlinear matrix equation XA+XBX= HX are investigated deeply. The sufficient and necessary conditions under which this equation has full rank solutions are proposed. The contents of this section will be helpful to discuss the following problems. Based on these obtained sufficient and necessary conditions, a mistake in [1] is pointed out.Secondly, the regulation problem for a class of square descriptor systems with constrained states and controls is considered. Based on the generalized inverse theory of matrices and the full rank solutions to the nonlinear matrix equation XA+ XBX=HX, the state-feedback control law is designed to guarantee that resultant closed-loop systems are admissible, and have a prescribed positively invariant set.Thirdly, for the above square descriptor systems, a counterexample is con-structed to show that a conclusion in [2] is not correct. By analyzing and studying this problem deeply, the reasonable assumptions are proposed. The obtained state-feedback control law can guarantee that resultant closed-loop systems are admissible, and have a positively invariant set, which corrects the mistake in [2].Fourthly, the regulation problem for a class of rectangular descriptor systems with constrained states and controls is studied. A dynamic compensator is designed to guarantee that resultant closed-loop descriptor systems are admissible, and have a positively invariant set which is a prescribed polyhedral set. We first translate the problem to that on square descriptor systems, and then the required dynamic compensator is designed by the method of solving the constrained regulation problem for square descriptor systems.The effectiveness of these designed methods proposed in this thesis are demon-strated by numerical examples and simulation results.