A probabilistic solution of robust H∞ control problem with scaled matrices

This paper addresses the robust H∞ control problem with scaled matrices. It is difficult to find a global optimal solution for this non-convex optimisation problem. A probabilistic solution, which can achieve globally optimal robust performance within any pre-specified tolerance, is obtained by using the proposed method based on randomised algorithm. In the proposed method, the scaled H∞ control problem is divided into two parts: 1 assume the scaled matrices be random variables, the scaled H∞ control problem is converted to a convex optimisation problem for the fixed sample of the scaled matrix and a optimal solution corresponding to the fixed sample is obtained; 2 a probabilistic optimal solution is obtained by using the randomised algorithm based on a finite number N optimal solutions, which are obtained in part 1. The analysis shows that the worst case complexity of proposed method is a polynomial.