Relaxed Stability Criteria Research Articles

Partitioning Technique for Relaxed Stability Criteria of Discrete-Time Systems with Interval Time-Varying Delay

We demonstrate an improved stability analysis based on a partition oriented technique for discrete-time systems with interval time-varying delay. The partition oriented technique introduces beneficial terms contributing to the negative definiteness of the Lyapunov function difference, meanwhile completely avoiding traditional inequality based approaches. In contrast, nonpartitioning oriented techniques do not put emphasis on further dividing the interval of the summation in the Lyapunov function. Herein, we demonstrate that the advantages of exploiting partitioning techniques manifest the relaxed stability criteria, as well as the flexibility to tune tradeoff between allowable timedelay range performance and computational load. Simulation carried out on a benchmark discrete-time system reveals the significant improvement in terms of maximum allowable upper bound in comparison.

An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation

A method is proposed to improve the numerical dispersion characteristics for simulations of the scalar wave equation in 3D using the FDTD method. The improvements are realized by choosing a face-centered-cubic (FCC) grid instead of the typical Cartesian (Yee) grid, which exhibits non-physical distortions of the wavefront due to the FD stencil. FCC grids are the logical extension of hexagonal grids in 2D, and have been shown previously to provide optimal sampling of space based on close packing of spheres (highest density). The difference equations are developed for the wave equation on this alternative grid, and the dispersion relationship and stability for grids of equal and non-equal aspect ratios are derived. A comparison is made between FCC and Cartesian formulations, based upon having an equal volume density of gridpoints in each method (i.e. the computational storage requirements of each method would be the same for the same simulated space). The comparison shows that the FCC grid exhibits a much more isotropic dispersion relation than the Cartesian grid of equivalent density. Furthermore, for an equivalent density, the FCC method has a more relaxed stability criterion by a factor of approximately 1.35, resulting in a further reduction in computational resources.

A Relaxed Stability Criterion for T–S Fuzzy Discrete Systems

Stability conditions for Tanaka-Sugeno (T-S) fuzzy discrete systems based on a single quadratic Lyapunov function or a weighting dependent Lyapunov function have been mentioned in lots of literature. The existence of a common matrix P is required in the former, and r (rules' number) positive matrices satisfying r2 Lyapunov inequalities are necessary in the latter. In this paper, the weighting dependent Lyapunov function is used again. Moreover according to the idea of the firing rule group and the distance estimation between two successive states of the system, the relaxed stability criterion of T-S fuzzy discrete system is proposed.

Stability criterion for radial wave equation infinite-difference time-domain method

A relaxed time-step stability criterion is derived for the radial wave equation in Schelkunoff form approximated by a finite-difference time-domain (FDTD) method. The criterion is established by comparing with the Cartesian Laplacian operator. This is the first step in developing stability analysis for a spherical wave implementation in FDTD.

Notes on a finite differencing scheme for the dispersion equation

Finite difference techniques applied to atmospheric dispersion problems often encounter time step limitations due to the variance in the characteristic length scales (horizontal to vertical) of both the field variables and the computational region. Methods to maximize the integration time step are explored and techniques are described which ensure numerical accuracy and stability of these optimized time step techniques. To circumvent time step limitations arising from consideration of the vertical diffusion term in the dispersion equation, a column implicitization technique is suggested which, through correction terms added to the differencing equation to compensate for truncation errors, provides an efficient and economical atmospheric dispersion solver which is insensitive to the common time step limitations of explicit schemes when large aspect ratio computational volumes are required. Further, it is shown that a relaxed stability criteria proposed by Leonard and Clancy for explicit differencing of the horizontal terms in the dispersion equation, presents a further saving in computational time provided correction terms to the differencing equation are included to eliminate phase and amplitude errors resulting from the larger time steps employed.