This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. This new algorithm ca...

We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the band is sufficiently wide (W ≫ N5/6). Otherwise, a different limiting distribution appears.

We study the properties of stationary G-chains in terms their generating functions. In particular, we prove an analogue Szeg\H{o} limit theorem for symplectic eigenvalues, derive expression entropy rate quantum Gaussian processes, and distribution eigenvalues truncated block Toeplitz matrices. also introduce a concept numerical range, analogous to that some its basic properties, mainly context ...

Recently reclaimed importance of the empirical distribution function of the eigenvalues of Wishart matrices was attached to the analysis of MIMO systems in [1]. But for the analysis of MIMO systems with signal processing at the transmitter [2] it is necessary to know the empirical distribution function of the inverse eigenvalues and the first and second moment of these distributions. We extend ...