Controllability and observability of hybrid discrete-continuous systems in the simplest function classes

作者：Marchenko V M^*

来源：Differential Equations, 2015, 51(11): 1461-1475.

DOI：10.1134/S0012266115110075

We consider controllability problems for linear discrete dynamical systems in the class of outputs of linear discrete dynamic controllers. We obtain a number of necessary conditions, sufficient conditions, and necessary and sufficient conditions for such a controllability. In the case of the solvability of some controllability problem, we represent the form of an admissible control bringing the trajectory of the system from an initial state into a given terminal state. Dual observability problems are stated, and the duality principle in considered problems of control and observation is proved. The obtained results are analyzed and illustrated in detail by related examples and counterexamples and are applied to the study of the controllability and observability problems for quantized hybrid discrete-continuous systems in classes of functions piecewise constant on the quantization interval and described by discrete algebraic and trigonometric polynomials as well as solutions of difference equations. We consider an example of the controllability of a hybrid discrete-continuous system in the class of algebraic polynomials.

• 出版日期2015-11