In the theory of dynamical systems, a linear time-invariant system is marginally stable if every eigenvalue in the system's transfer-function is non-positive, and all eigenvalues with zero real value are simple roots. In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ... A linear system is a model based on some kind of linear operator. ... A time-invariant system is one whose output does not depend explicitly on time. ... In mathematics, a number is called an eigenvalue of a matrix if there exists a nonzero vector such that the matrix times the vector is equal to the same vector multiplied by the eigenvalue. ... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ... A negative number is a number that is less than zero, such as −3. ...