Sentence examples for mean square defined from inspiring English sources

One of the aim of this paper is to show that in the general case of discretetime time-varying linear stochastic systems subject to an homogeneous or an inhomogeneous Markov chain, exponential stability mean square defined in terms of state space trajectories of the systems cannot be always characterized via quadratic Lyapunov functions.

The mean square defined in (12) at the top of D″-layer of the forecasts y f (the dashed line) and of the observations y (the solid line) from 1994 to 2002.

The general form of the MLS interval is a function of the observed mean squares, and can be written: where L and U are functions mapping 3-dimensional space to one-dimensional space, and, and are mean squares defined in Table  1.

Nonlinear continuous-time 2D systems described by a Roesser model and nonlinear discrete-time repetitive process with Markovian jumps are considered, for which global asymptotic stability in the mean square is defined and sufficient conditions for the existence of this property obtained in terms of stochastic vector Lyapunov functions.

Specifically, we plot the mean square error (defined as ).

MSD is the mean square displacement defined as: mathrm{M}mathrm{S}mathrm{D}=<left[ r(t)- rleft {t}_0right)right]hat{mkern6mu} 2> (2).

Root mean square (RMS), defined as the square root of the mean square value for the EMG was calculated [ 29, 33] and used to assess possible voluntary movement to the motion by the participant.

it is defined on the class ξ, i.e., it is a linear system of the form (10), and. the real matrix (K t)) is chosen to minimize the symmetrized mean squares error defined as follows Jbigl(K t bigr):=operatorname{Tr}bigl[P t bigr], (11) where (P t)) is the symmetric error covariance matrix defined by P t):=C_{e(t)}=frac{1}{2} mathbb{E}_{rho}bigl[ e(t) e(t)^{T}+bigl(e(t)e(t)^{T}bigr)^{T} bigr].

Performance was measured using the mean square error (MSE) defined as MSE n = E e M − 1 2 n and the excess mean square error (EMSE) defined as E M S E(n)=E{(e M−1(n)−s(n))2} [17].

where MSE (Mean Square Error) is defined by.

The root mean square error is defined as RMSE =  σ 2 ^.