Discrete- time systems and difference algebra. (Automatique en temps discret et algèbre aux différences.) (French) Zbl 0706.93039

Fliess, Michel

Forum Math. 2, No. 3, 213-232 (1990).

Summary: A new theory of discrete-time linear and nonlinear systems, based on difference algebra, is presented. Many new results are obtained concerning the definition of input and output, invertibility, realization and causality, feedback synthesis for decoupling and linearization. The old question concerning the relationship between continuous-time and discrete-time systems, which up to now was not clarified in the nonlinear case, is completely elucidated here since our approach in many respects mimics what has been done for continuous-time systems with differential algebra [see the author, ibid. 1, No.3, 227-238 (1989; Zbl 0701.93048)].

MSC:

93C55	Discrete-time control/observation systems
12H10	Difference algebra
39A10	Additive difference equations
93A99	General systems theory
93C05	Linear systems in control theory
93C10	Nonlinear systems in control theory

Keywords:

input; output; invertibility; realization; causality; feedback synthesis; decoupling; linearization

Citations:

Zbl 0701.93048