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Positive Control for a Class of Nonlinear Positive Systems
In this contribution, we focus on a class of nonlinear positive systems, arising especially in biological processes. These are SISO input-affine...
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A Simple Food Chain Model with Delay
In this paper we consider a chemostat-like model for a simple food chain of microorganisms. This consists of a well stirred nutrient substance that...
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Reachability and Invariance Problems in Max-plus Algebra
We present a synthesis of recent results concerning reachability and invariance problems for max-plus linear dynamical systems. Semigroup membership...
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Nonnegative Infinite Hankel Matrices having a Finite Rank
A nonnegative infinite Hankel matrix is an infinite Hankel matrix which has nonnegative entries. The paper studies the relationship between rational...
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Unforced Continuous Petri Nets and Positive Systems
Petri nets (PNs) are a well-known family of formalisms whose definition immediately sets them, in a broad sense, as positive systems. Although they...
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B Appendix: The Continuous DLMI Method
In the past, LMIs were used mainly to solve stationary problems. The algebraic nature of the Riccati equations to which these problems correspond,...
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5 Continuous-time Systems: Static Output-feedback
The static output-feedback problem has attracted the attention of many in the past [5], [111] and [100]. The main advantage of the static...
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9 Discrete-time Systems: Tracking Control
A method for solving the deterministic discrete-time tracking problems with preview has been introduced in [17]. Similarly to the deterministic...
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8 Discrete-time Systems: General Filtering
In Chapter 7 we introduced the solution to the output-feedback control problem for the time-varying, discrete-time systems with state-multiplicative...
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1 Introduction
This monograph considers linear systems that contain, in the general case, state, control and measurement multiplicative noise, in both the...
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2 Continuous-time Systems: Control and Luenberger-type Filtering
In this chapter we address the problems of continuous-time, state-multiplicative, H∞ state-feedback control and estimation via the solution of the...
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A Reconstruction Algorithm for Gene Regulatory Sparse Networks using Positive Systems
In this paper we propose a new gene network reconstruction (or identification) scheme which takes advantage of the sparseness of a gene network using...
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Competitive and Cooperative Systems: A Mini-review
The theory of competitive and cooperative dynamical systems has had some remarkable applications to the biological sciences. The interested reader...
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A Feedback Perspective for Chemostat Models with Crowding Effects
This paper deals with an almost global stability result for a chemostat model with including effects. The proof relies on a particular small-gain...
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Positive Particle Interaction
This paper treats interaction between finitely many particles where the future state of each particle is obtained from the present states of all...
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Blending Positive Matrix Pencils with Economic Models
We consider E(x)x(k + 1) = F(k)x(k), $k \in Z^+_0$ , where E(k) and F(k)...
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A Paradigm for Derivatives of Positive Systems
We develop a framework for differentiation of positive operators, such as Markov kernels, through interpreting derivatives of positive operators as...
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Some Recent Developments in Positive 2D Systems
Necessary and sufficient conditions for the reachability and controllability of positive 2D Roesser model are established. It is shown that the...
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Nonlinear Positive 2D Systems and Optimal Control
In the paper, a nonlinear positive 2-D control system given by the Goursat-Darboux problem is considered. First, we give sufficient conditions for...
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Small-gain Theorems for Predator-prey Systems
We present a global stability result for Lotka-Volterra systems of the predator-prey type. It turns out that these systems can be interpreted as...