Sentence examples for by constructing the appropriate from inspiring English sources

By constructing the appropriate Lyapunov Krasovskii functional using the available information about the actual sampling pattern, a new set of sufficient condition is obtained to guarantee that the singular networked cascade control systems to be admissible and strictly (Q,S,R -dissipative.

In Section 3, the main results of global robust exponential synchronization are obtained by constructing the appropriate Lyapunov functional and applying inequality skills.

(2.19) Similarly, by constructing the appropriate coefficient matrix (H_{j}) to guarantee ({{dot{V}}_{j}}<0), the error dynamic systems (e_{j}(t)) will be asymptotically stable, that is, the adaptive synchronization between the j system and the (j+1) system is realized.

By constructing the appropriate coefficient matrix (H_{1}), one can guarantee ({{dot{V}}_{1}}<0), then the error dynamic systems (e_{1}(t)) is asymptotically stable, that is, the adaptive synchronization between the first system and the second system is achieved.

We predict the phenotype Y j, k, s), for a future individual with mother j, father k, and sex s, by constructing the appropriate design matrix x jks and using the Gibbs samples to estimate the posterior predictive mean Y ^ (j, k, s ) = 1 T ∑ t x j k s T β (t ) of all draws t ∈ 1, … ,  T.

We visit some basic properties of this discrete model and we study the stabilities of the equilibria by constructing some appropriate Lyapunov functional for the endemic equilibrium.

This is the L2-gain of the system, for which we can again obtain an upper bound by constructing an appropriate storage function S. To do so, given the appropriately normalized system (2) and ε > 0, we assume that the trajectories with input u with || u||2 = ε and initial condition 0 remain in a region D around the steady state (the origin) for all time.

The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for disease-free equilibrium and by applying geometrical approach to chronic infection equilibrium.

Then, by constructing an appropriate Lyapunov's functional, we establish the main result which is the global and asymptotic stability of this model.

The boundary value problem of interest is solved by constructing an appropriate set of multipole functions which satisfy the governing differential equations in each half-space and the boundary conditions along the interface between the two half-spaces.

By constructing an appropriate Lyapunov functional and using the average dwell time scheme, a novel delay-dependent sufficient condition for the solvability of the H∞ filtering problem is derived.