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The paper considers a model of co-generation with distributed parameters, described by a non-standard boundary value problem with nonlinear boundary conditions with respect to a system of conservation laws. For the aforementioned model, well posedness in the sense of Hadamard, existence of some invariant sets, equilibria and their stability will be studied. The stabilising feedback laws are synthesised using a suitably constructed Lyapunov functional. [ABSTRACT FROM AUTHOR]

The paper considers the standard nuclear reactor model with pointwise active zone dynamics together with the dynamics of the external circuits of the reactor in the linearised version. There are presented some Lyapunov functions and the corresponding stability theorems. These Lyapunov functions can be used in synthesising feedback controllers for the reactor power. Two cases - the control Lyapunov function and the sliding mode control - are considered. It is shown that the same Lyapunov functions used in synthesis can be used to obtain stability of the closed-loop reactor-controller. [ABSTRACT FROM AUTHOR]