Algebraic entropy for semi-discrete equations

A new positive definite semi-discrete mixed finite element solution for parabolic equations

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

Realization Theory for Discrete-Time Semi-algebraic Hybrid Systems

We present realization theory for a class of autonomous discrete-time hybrid systems called semi-algebraic hybrid systems. These are systems in which the state and output equations associated with each discrete state are defined by polynomial equalities and inequalities. We first show that these systems generate the same output as semi-algebraic systems and implicit polynomial systems. We then ...

Discrete Time H∞ Algebraic Riccati Equations

Semi-implicit Krylov deferred correction methods for differential algebraic equations

In the recently developed Krylov deferred correction (KDC) methods for differential algebraic equation initial value problems [33], a Picardtype collocation formulation is preconditioned using low-order time integration schemes based on spectral deferred correction (SDC), and the resulting system is solved efficiently using Newton-Krylov methods. KDC methods have the advantage that methods with...

Minimax state estimation for linear discrete-time differential-algebraic equations

This paper presents a state estimation approach for an uncertain linear equation with a non-invertible operator in Hilbert space. The approach addresses linear equations with uncertain deterministic input and noise in the measurements, which belong to a given convex closed bounded set. A new notion of a minimax observable subspace is introduced. By means of the presented approach, new equations...