This article provides the formulas connecting Laguerre spectrum of output signal a linear discrete-time time-invariant delay system to its input signal. The Laguerre-domain representation is meaningful when square summable, and stable. A certain type polynomials arising in evaluation due presence time defined, key properties these are investigated. characterized by three-term recurrence relatio...

In this paper, we investigate the properties of Schwarz matrix, a specific type matrix that appears in stability analysis discrete-time linear time-invariant systems. We derive formula for determinant and its permanent. also provide conditions on entries ensure system described by state update equation $x_{k+1} = Bx_k$ is stable, as well guarantee eigenvalues are real. These findings insights i...

A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises covariance. Safety characterized using polytopic constraints on the states and control inputs. The empirically learned model process noise covariance their confidence bounds are used construct a robust optimization problem minimally modifying nominal actions...