This paper addresses the issues of conservativeness and computational complexity of robust control. A new probabilistic robust control method is proposed to design a high performance controller. The key of the new method is that the uncertainty set is divided into two parts: r‐subset and the complementary set of r‐subset. The contributions of the new method are as follows: (i) a deterministic robust controller is designed for r‐subset, so it has less conservative than those designed by using deterministic robust control method for the full set; and (ii) the probabilistic robustness of the designed controller is evaluated just for the complementary set of r‐subset but not for the full set, so the computational complexity of the new method is reduced. Given expected probability robustness, a pertinent probabilistic robust controller can be designed by adjusting the norm boundary of r‐subset. The effectiveness of the proposed method is verified by the simulation example.

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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.

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