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Right and left invertibility of nonlinear control systems. (English) Zbl 0719.93038

Nonlinear controllability and optimal control, Lect. Workshop, New Brunswick/NJ (USA) 1987, Pure Appl. Math., Marcel Dekker 133, 133-176 (1990).
[For the entire collection see Zbl 0699.00040.]
This paper discusses the invertibility problem for control systems assumed to be nonlinear. First the author gives a list of equivalent conditions for left and right invertibility of a linear system (with no feedthrough term). These conditions involve such notions (for the right invertible case) as right invertibility of the transfer function, number of zeros at infinity, existence of a linear differential relation among the components of the output which is independent of the initial state and of the input, reproducibility of an arbitrary output function for each fixed initial state by appropriate choice of input function, and surjectivity of the input-output map. Dual equivalent conditions are given for the left invertibility issue. Extensions of these various notions to the nonlinear setting (to the extent possible) and their equivalence with left/right invertibility of a nonlinear system are then discussed. The main tool is the extension algorithm of the author and Nijmeijer developed to handle the dynamic disturbance decoupling problem for nonlinear systems. Also discussed are connections with the differential algebraic approach to nonlinear system theory recently introduced by Fliess.

MSC:

93C10 Nonlinear systems in control theory

Citations:

Zbl 0699.00040