Sentence examples for by constructing an appropriate from inspiring English sources

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.

Then, we further consider the case of asymmetric time-varying output constraints by constructing an appropriate BLF.

By constructing an appropriate Lyapunov Krasovskii functional and applying Wirtinger-based inequality for discrete-time context combined with reciprocally convex approach, an improved stability criterion is obtained.

By constructing an appropriate Lyapunov functional, some sufficient conditions are derived under which the estimation error dynamics is stochastically stable and the H∞ performance constraint is satisfied.

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.

Subsequently, a sufficient condition for the leader-following consensus of NMTS is derived in the form of linear matrix inequality (LMI) by constructing an appropriate Lyapunov Krasovskii functional and by utilizing some matrix and integral inequality techniques.

By constructing an appropriated Lyapunov function and employing average impulsive interval (AII) method, some FTS criteria for the nonlinear impulsive sampled-data systems are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox.

By constructing an appropriated function, some sufficient conditions are derived to guarantee the FTS of the addressed linear non-autonomous systems.

In this section, we shall investigate the FTS of the linear non-autonomous system by constructing an appropriated function and using the Metzler matrix method.

By constructing an appropriated function, we derive some explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre-specified finite time interval.

Then, by constructing an appropriated common Lyapunov function and by resorting to the Kotelyanski lemma [52] and the M-matrix proprieties [53, 54], new delay-independent stability conditions under arbitrary switching law are deduced.