Improved Solvable Condition for H∞ Control Problem via State Feedback
ZENG Jian-ping1, CHENG Peng1, ZHANG Li-jun2*
1. Beijing University of Aeronautics and Astronautics, School of Automation Science and Electrical Engineering;
2. Beijing University of Aeronautics and Astronautics, Dept. of Computer Science and Engineering
Simplified solvable condition for H∞ control problem via state feedback is considered. The solvability of H∞ control problem via state feedback is considered to be equivalent to that of a class of linear matrix inequality (LMI). It can reduce the variable dimension by deleting redundancy matrix variables for the class of LMI, and a dimension-reduced LMI is obtained then. Moreover, the feasible solution set to the former LMI can be reconstructed via that of the latter. On the above basis, an improved solvable condition for H∞ control problem via state feedback is deduced. The H∞ controller set can be constructed by the feasible solution to the simplified solvable condition, and it also has more plentiful free parameters. Finally, two simple examples are given to show the validity of this approach.