Nonlinear systems research based on LPVs has been got more and more concern. Fist, the system should be changed into a linear parameter-varying system model; then, using existed linear design methods to attain the analyses and design.Compared with the tranditonal means, the new method based on LPVs can avoid the linearization of the some importand subsections and directly get the global performance,moreover, the new method can solve some problems which can not be work out by the old method. Because of the analysis and design referring with the parameter varying, the conservation of the performance decreased. In result, the analysis and design based on LPVs has becomed a very effective tool to deal with the nonlinear plant.However, the LPVs mode bring with the difficulty of computation because of the infinite-dimensional. In general , there are four methods to solve the infinite-dimensional, and they are as the following: 1. the polytopic method , in which we only solve the vertex of the parameter, we can work out the whole problem; 2. the multiconvexity method; 3. the basis fuctions with the gridding technique; 4. the linear faractional transformation(LFT) with small-gain theorem.Using the Projection Lemma and with the help of some slack matrices, the parameter-dependent Lyapunov functions matrices and the system matrices are decouple so that the condition of the solution is obtained.The papers is organised as two parts as follows.Partâ… : Gain-scheduling1. The performance analysis of the LPVs through the multiconvexity method.2. The sate feedback design of the LPVs and3. The pole assignment design of the LPVs by means of the multiconvexity method.4. The filtering design of the LPVs by means of the multiconvexity method.Partâ…¡: Fault detection1. The fault detection design through the basis functions with gridding technique.2. The fault detection design by using of polytopic technique.3. The fault detection design based on multiconvexity means. |