×

zbMATH — the first resource for mathematics

Application de la théorie des systèmes implicites à l’inversion des systèmes. (French) Zbl 0556.93026
Analysis and optimization of systems, Proc. 6th int. Conf., Nice 1984, Part 2, Lect. Notes Control Inf. Sci. 63, 142-156 (1984).
[For the entire collection see Zbl 0538.00036.]
We first recall the definition of an implicit system (sometimes also called ”generalized state-space system”) and its most important properties. We then define the notion of inverse system, proving existence and uniqueness from an external point of view. Next we show how the theory of implicit systems yields inverse systems and some of their properties in an easy way. For instance we examine the conditions under which the inverse system is minimal, and show also that a state-space system is right or left invertible if some blocks are missing in its Kronecker form.

MSC:
93B99 Controllability, observability, and system structure
34A99 General theory for ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
93B20 Minimal systems representations