In Shallit’s problem (SIAM Review, 1994), it was proposed to justify a two-term asymptotics of the minimum rational function $$n$$ variables defined as sum special form whose number terms is order $$n^2$$ $$n\to\infty$$ . Of particular interest second term this (“Shallit’s constant”). The solution published in SIAM Review presented an iteration algorithm for calculating constant, which conta...

In this paper, it is shown that by exploiting the explicit parametric state feedback solution, it is feasible to obtain the ultimate solution to minimum sensitivity problem. A numerical algorithm for construction of a robust state feedback in eigenvalue assignment problem for a controllable linear system is presented. By using a generalized parametric vector companion form, the problem of eigen...

Transmit waveform design is one of the most important problems in active sensing and communication systems. This problem, due to the complexity and non-convexity, has been always the main topic of many papers for the decades. However, still an optimal solution which guarantees a global minimum for this multi-variable optimization problem is not found. In this paper, we propose an attracting met...