On the local qualitative behavior of differential-algebraic equations

Fuzzy Local Fractional Differential Equations

Differential Equations ( Qualitative Differential Equations ) Qualitative Constraints Qualitative Simulation

ion Perturbation Statistical Analysis (e.g. Regression Methods) Dynamic System System Behavior Quantitative System Behavior Qualitative System Behavior (Qualitative States) (Numerical Data) Inductive Learning (e.g. GENMODEL) Figure 1. Qualitative reasoning is an abstraction of mathematical reasoning with di erential equations and continuously di erentiable functions. and an initial state, we ca...

Analysis of Transient Behavior in Linear Differential Algebraic Equations

The linearized Navier-Stokes equations form a type of system called a differential algebraic equation (DAE). These equations impose both algebraic and differential constraints on the solution, and present significant challenges to solving. This paper discusses a method for solving DAEs by the Schur factorization to avoid some of the obstacles that are typically present. We also investigate the ...

Nonsmooth Differential-algebraic Equations

A nonsmooth modeling paradigm for dynamic simulation and optimization of process operations is advocated. Nonsmooth differential-algebraic equations (DAEs) naturally model a wide range of physical systems encountered in chemical engineering conventionally viewed as exhibiting hybrid continuous/discrete behavior. Due to recent advancements in nonsmooth analysis, nonsmooth DAEs now have a suitabl...

Switched differential algebraic equations

In this chapter an electrical circuit with switches is modeled as a switched differential algebraic equation (switched DAE), i.e. each mode is described by a DAE of the form Ex′ = Ax+Bu where E is, in general, a singular matrix and u is the input. The resulting time-variance follows from the action of the switches present in the circuit, but can also be induced by faults occurring in the circui...