For any two symmetric positive semidefinite matrices and, such that and positive semidefinite matrix, the integral is nonnegative (where is any path from to ).
Thus in our case, where are matrices, and the integral over a path from to is equivalent to the following line integral: (A4).
A set of new sufficient conditions is developed which not only guarantees the stochastic admissibility of the sliding mode dynamics, but also determines all the parameter matrices in the integral sliding function.
However, for the receiver I/Q imbalance closed form solutions are exist, for generic covariance matrix the integrals above are not solvable in closed forms (when transmitter I/Q imbalance is very small then ρΔ → 0 and hence the distribution of the displacement vector follows (20)).
The second pair of summation is over basis functions, φ i. P is the density matrix, and the integral reflects the Columbic interactions between the electrons and the point charge.
Because analytical solutions of integro-differential equations are difficult, therefore, numerical methods can be effectual such as hybrid Euler Taylor matrix method, the integral mean value theorem, non-standard finite difference, and multi-wavelet Petrov Galerkin method in [4, 10, 11, 13], respectively.
There are two main techniques for dealing with the integrals that appear in the derivative: the free-weighting matrix method and the integral inequality method.
Since the Schur product preserves the positive definite/semidefinite quality [20, 7.5.3], it is easy to see that when, both are symmetric, and since is a positive semidefinite matrix for all, the integral is always nonnegative.
By introducing the free weighting matrices to deal with the integral items and converting the coupling time-varying matrix inequalities into a group of decoupling matrix inequalities, an innovative delay-dependent stabilization criterion is first presented.
By introducing some free weighting matrices to deal with the integral items and converting the coupling time-varying matrix inequalities into a group of decoupling matrix inequalities, a new delay-dependent stabilization criterion is firstly presented.
