In this paper, we establish the total controllability and observability results for a dynamic system with non‐instantaneous impulses on time scales in a finite dimensional space
Rn. This paper consists of two segments: the first segment of the work is concerned with total controllability and the other segment with total observability analysis. The tools for study include variation of parameter and Gramian matrix. Some theoretical as well as numerical examples with simulation for two time scales
double-struckT=double-struckR and
double-struckT=P1,1 are given to illustrate the application of these results.
In this paper, we establish some necessary and sufficient conditions of the controllability results for a class of impulsive switched systems with noninstantaneous jumps on time scales. Firstly, we define the solution of the considered problem by using the parameter variation method. We also define some Gramian matrices to establish the controllability results. Moreover, we give some conditions under which the time invariant impulsive switched system is totally controllable. At the end, we provide one numerical example for different time scales to validate the obtained analytical results.
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