Abstract: A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N -th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is ...

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

This paper presents the Python implementation of an interval system in the extended real set that is closed under arithmetic operations. This system consists of the lattice generated by union and intersection of closed intervals, with operations defined by image closure of their real set counterparts. The effects of floating-point rounding are accounted for in the implementation. Two applicatio...

Significant beam intensity-dependence of the vertical emittance growth was experimentally observed at the Accelerator Test Facility (ATF) at KEK extraction beamline. This paper presents the simulations of possible vertical emittance growth sources, particularly in the extraction channel, where the magnets are shared by both the ATF extraction beamline and its damping ring. The vertical emittanc...

Many problems in optimization theory are strongly nonlinear in the traditional sense but possess a hidden linear structure over suitable idempotent semirings. After an overview of ‘Idempotent Mathematics’ with an emphasis on matrix theory, interval analysis over idempotent semirings is developed. The theory is applied to construction of exact interval solutions to the interval discrete stationa...

This paper details a technique, called inter-block backtracking (IBB), which improves interval solving of decomposed systems with non-linear equations over the reals. This technique, introduced in 1998 by Bliek et al., handles a system of equations previously decomposed into a set of (small) k × k sub-systems, called blocks. All solutions are obtained by combining the solutions computed in the ...

The problem of characterizing in a guaranteed way the set of all feasible set-points of a control problem is known to be difficult. In the present work, the problem to be solved involves non-linear equality constraints with variables affected by logical quantifiers. This problem is not solvable by current symbolic methods like quantifier elimination, which is commonly used for solving this clas...

We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation sol...