The Strict Positive Realness (SPR) of a transfer function is an important performance in control system and much attention has been paid. However, most of the results belong to SPR analysis. From the engineering point of view, synthesis problem is more practical and is still a challenging topic. These papers focus on the developing algorithms for the Robust SPR synthesis. The content of this paper goes as follows: Firstly, researches on robust control and SPR are reviewed, the concepts and properties are described, and the architecture of this thesis are introduced. Secondly, for randomly high order polynomial families with uncertainty, we present an algorithm for robust SPR synthesis based on genetic algorithm, which is effective for polynomial sets such as segment, interval and polygon polynomial sets. The algorithm can be extended easily to the strength SPR problem and discrete systems. Examples illustrate its effectiveness. Thirdly, a new geometry algorithm based on order reduction for SPR synthesis is presented. By searching from the boundary of the region of the weak Strict Positive Realness (WSPR) of a polynomial, we can find the boundary of the WSPR intersection region of the polynomial family, and then transfer the SPR synthesis problem to a feasible problem with just two variables, thus simplifying the problem and saving the computation. The conditions we get by the algorithm can be satisfied for the lower order polynomial segment (n≤5) and interval (n≤4) polynomial sets. Examples also illustrate its effectiveness. Fourthly, an algorithm based on alternating projection has been presented. We describe the SPR problem by Linear Matrix Inequalities (LMIs), then for several special SPR problems, we formulate them as feasibility problems with simple matrixes constraint sets, by obtaining the analytical expressions for the orthogonal projection operators onto these sets, we try to obtain the solution. A conclusion is given finally.
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