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4 Compositional Modelling of Distributed-Parameter Systems
The Hamiltonian formulation of distributed-parameter systems has been a challenging reserach area for quite some time. (A nice introduction,...
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A On the Literature’s Two Different Definitions of Uniform Global Asymptotic Stability for Nonlinear Systems
In this appendix we discuss two different deffnitions of uniform global asymptotic stability (UGAS), both used in the literature. In the first one,...
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Two‐Fluid Approach: Example of Awe's Model
Two‐fluid descriptions often use explicitly separate treatments for the conservation equations in each fluid, along with expressions for exchange...
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Conclusion, Future Modeling Trends
The relevance of this study stands not in the topics that have been discussed, since most of them have already been explored for many years now, but...
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Comparison of Single and Two‐Fluid Approaches
The results of the “0D„ analyses gathered in Tables 5.1 and 6.1 and discussed in Sects. 5.3 and 6.2 provide the basis for comparing Dam's к–ε and...
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Specific Treatment of Shocks: Constraints on Models1
Before examining the phenomenology of the interaction between a shock and turbulent or material heterogeneities, it is useful to recall that the...
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2 Observer Design for Nonlinear Systems
In this chapter, an overview of main observability problems and possible observer designs for nonlinear systems is proposed. In particular the...
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Single‐Fluid Approach: Example of Dam's к–ε Model
The statistical equations for the turbulent flow of an incompressible fluid are found in the literature [58], but they are adapted here to the...
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6 Structural Properties of Discrete and Continuous Linear Time-Varying Systems: A Unified Approach
The aim of this chapter is the study of structural properties of linear systems. Systems with time-varying coefficients are considered, both in the...
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1 Nonlinear Adaptive Stabilization via System Immersion: Control Design and Applications
This chapter presents a review of a recently developed methodology for the (adaptive) stabilization of nonlinear systems via state and output...
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5 Algebraic Analysis of Control Systems Defined by Partial Differential Equations
The present chapter contains the material taught within the module P2 of FAP 2004. The purpose of this intensive course is first to provide an...
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1 Introduction to Nonlinear Optimal Control
The maximum principle is presented in the weak and general forms. The standard proofs are detailed, and the connection with the shooting method for...
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3 Sampled-data Control of Nonlinear Systems
This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring...
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4 Stability Analysis of Time-delay Systems: A Lyapunov Approach
This chapter is devoted to the stability problem of time-delay systems using time-domain approach. Some basic concepts of time-delay systems are...
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7 Structural Properties of Linear Systems – Part II: Structure at Infinit
This chapter is the sequel of [7]. Its topic is the structure at infinity of discrete and continuous linear time-varying systems in a unified...
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5 Controllability of Partial Differential Equations
In this section, we recall some basic elements of semigroup theory (see [25]). In particular, all the arguments of the results mentioned below can be...
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6 Stability, Told by Its Developers
Lyapunov stability theory is probably the most useful qualitative method to study the behaviour of dynamical systems; it benefits from at least 75...
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Review of Different Instability Types and Regimes
The three major types of “ideal„ instabilities studied here are [92]:
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Introduction
Many Dam applications involve phenomena of hydrodynamic mixing instabilities at interfaces between different materials. Simulation codes must include...