Sentence examples for matrix of dynamics from inspiring English sources

It is also taken into account as motivation that unforced linear time-invariant dynamic systems are exponentially stable to the origin if the matrix of dynamics is a stability matrix.

Note that the closed-loop matrix of dynamics at the j n -sample is similar by a similarity transformation to its companion block partitioned form in (3.10).

The stability conditions are basically concerned with the matrix measure of the delay-free matrix of dynamics to be negative and to have a modulus larger than the contribution of the error dynamics with respect to the limiting one.

The stability degree is defined by the modulus of the dominant eigenvalue of the matrix of dynamics if the dominant eigenvalue is simple and such a number is a strict upper-bound of the stability degree, otherwise.

The dynamic system is stabilizable (or, simply, the pair is stabilizable) if and only if Its meaning is that there exists such that the matrix of dynamics of the closed-loop feedback system is a stability matrix; that is, and any state-trajectory solution with bounded initial conditions is uniformly bounded and converges asymptotically to the zero equilibrium, as a result.

The result is achievable irrespective of the norms of the incremental matrices of dynamics of (2.1) with respect to its limiting equation.

The coefficient matrix of the error dynamics between each pair of synchronized systems is chosen such that the number of active control functions reduces from two to one, thereby, significantly reducing controller complexity in the design.

Assuming that a disturbance enters into a system independently of the control input signals, the method makes it possible to identify a denominator polynomial matrix of the disturbance dynamics, and then to design an H∞ controller suppressing the effect of the disturbance.

For the proposed compartmentalization, its value can be obtained for GLEaM by evaluating the largest eigenvalue of the Jacobian or next generation matrix of the infection dynamics in a disease-free equilibrium [ 45], yielding R0 = βμ-1(1 - p a + r β p a ) if the age structure is not considered.

Using the semi-tensor product of matrices, the dynamics of a Boolean control network is expressed in its algebraic form.

As an example, Sengers et al. [ 3] in their review concentrated on the contribution of computational modeling as a framework to obtain an integrated understanding of key processes including nutrient transfer, matrix formation, dynamics of cell population, cell attachment and migration, and local mutual interactions between cells.