Linear Systems

11.3.3  Summary of the Approach

The search for satisfactory solutions may be very difficult when the SLPMM algorithm acts on a module of very high dimension. Because the initialization step is important for an iterative algorithm, therefore, in order to overcome this difficulty, a new initialization step for obtaining an initial solution is proposed by combining it with the non-fragile controller design method.

Based on the above analysis, instead of using initialization step as Step 2 of Algorithm 11.1, we have the following algorithm to obtain the initial solution of the SLPMM algorithm.

Algorithm 11.2

Step 1. By solving the optimization problem (11.40), the non-fragile controller gain matrices $\tilde{A},\tilde{B}$, and $\tilde{C}$ can be obtained.

Step 2. Obviously, ...