Synthesizing the Static Feedback Gain Matrix to Minimize the System H Infinity Norm Using Linear Matrix Inequality Approach

Abstract

In this paper, I propose a method to syn-thesize a static state feedback gain matrix to minimize the system H infinity norm using linear matrix inequality (LMI) approach. To illustrate the result, an example using the dynamics of a double integrator is used. The final result shows that the solution achieved by LMI approach is the same as solution done manually. Furthermore, the LMI approach opens a direction to promote the sparsity structure of the feedback gain matrix.