OPERATION ON SETS AND IT'S APPLICATIONS TO COMPUTER AIDED DESIGN OF ROBUST CONTROL SYSTEMS

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Because of variation and uncertainty of system parameters, mathematical models Invariably give an imperfect description of real systems. Therefore, robustness is one of the most fundamental requirements for control systems. Main results of this research project may be summarized as follows:1. Polygon Interval Arithmetic. To treat uncertainty, we defined operations (addition, multiplication, and reversion) on sets consisting of all the convex polygons, which we call polygon interval arithmetic. We derived several important properties of polygon interval arithmetic. We also proposed an efficient algorithm to calculate addition of convex polygons.2. Robust Stability Analysis. (1)Stability of feedback systems can be analyzed by examining determinants of return differential matrix at every frequencies. A method based on the mapping theorem was used to calculate it, but it is very much time consuming. We proposed to use a method based on both polygon interval arithmetic and the mapping theorem to calculate determinants. (2)Stability of (nonlinear) systems can be examined by using Liapunov functions. We proposed a method to construct a Liapunov function via computational geometric technique to calculate convex hulls.3. RSRD(Robust Sequential Return Difference) method. We proposed RSRD method to design robust control systems, which uses polygon interval arithmetic, and which makes possible to design controllers of each loops "independently", and to guarantee the integrity.4. CAD(Computer Aided Design) System. We developed a CAD system to design robust control systems based on RSRD method. We also implemented a program to calculate stability margin of multi-input multi-output systems.