DIOPHANTINE EQUATIONS IN CONTROL - A SURVEY

This survey is also a tutorial whose aim is to explain the role of dio phantine equations in the synthesis of feedback control systems. These are linear equations in a ring and result from a fractional represent ation of the systems involved. The cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plan t. One can then choose, in principle, the best controllers for various applications. These ideas evolved from early attempts to use polynomi al equations in the design of discrete-time linear systems. By now the y have been extended to continuous-time, infinite-dimensional, time-va rying and non-linear systems.