Decentralized Robust Control Theory And Its Application Based On Structured Singular Value Approach

The structured singular value V is an important analysis and design method to resolve the structured uncertainty system. Applying the method to design controllers can reduce the conservation of the robust control system, and also give consideration to both the robust stability and the robust performance of the control system. Decentralized control is an efficient design method for complex control system and industrial large-scale system. Applying the method can reduce the amount of disposal information and the complexity of data communication. And more, it can realize feedback control quickly.The central problem for decentralized control is to design the decentralized controllers. Generally, we solve the problem by decentralized H~ control method. But the solution is conserve for the structured uncertainty interconnected large-scale system. To reduce the conservation of the system, we apply the structured singular value u to design the decentralized controllers of the system, and the research in the field is rare at present.The structured singular V problems are quite hard to solve. The traditional algorithm is D-K iteration. But the n problems are not convex in general, and hence it is difficult to find a global optimal solution. For state feedback, we resolve this problem in chapter 3 by transferring the decentralized n problems into the decentralized scaled H- control problem, then solve the problem by ILMI optimization problems. But the method cannot be applied for decentralized output feedback because of its no convex restriction. We resolve this problem in chapter 4 by submitting decentralized strongly robust H- performance criterion based on the quadratic stability theorem, then give the sufficient conditions for the existence of decentralized output feedback controller in terms of LMIs, at last, we compute the LMIs by cross iteration algorithm.We consider both state feedback and output feedback based on the structured singular value theory. To validate the correctness of the algorithm, we gave two numerical examples in the paper. Via the curves of simulation, we can know the feedback control system, which is made of our designing controllers, is perfect in the robust stability and the robust performance. Thus, it shows that our algorithm is feasible.