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**Well posedness of triples of operators (in the sense of linear systems theory).**
*(English)*
Zbl 0686.93049

Control and estimation of distributed parameter systems, 4th Int. Conf., Vorau/Austria 1988, ISNM 91, 41-59 (1989).

Summary: [For the entire collection see Zbl 0682.00026.]

A triple of operators (A,B,C) is called well posed if there exissts an abstract linear system having A as the generator of its semigroup, B as its control operator and C as its observation operator.

The main result of this paper is a set of necessary and sufficient conditions for (A,B,C) to be well posed. Essential use is made of the concept of transfer function and the theory is illustrated by two examples. In the second example we solve the delicate problem of modelling the one dimensional heat equation with Dirichlet boundary control and point observation with an abstract linear system.

A triple of operators (A,B,C) is called well posed if there exissts an abstract linear system having A as the generator of its semigroup, B as its control operator and C as its observation operator.

The main result of this paper is a set of necessary and sufficient conditions for (A,B,C) to be well posed. Essential use is made of the concept of transfer function and the theory is illustrated by two examples. In the second example we solve the delicate problem of modelling the one dimensional heat equation with Dirichlet boundary control and point observation with an abstract linear system.

### MSC:

93C25 | Control/observation systems in abstract spaces |

35B37 | PDE in connection with control problems (MSC2000) |