We investigate sufficient conditions for a discrete nonlinear non-homogeneous dynamical system to converge to consensus. We formulate a theorem which is based on the notion of averaging maps. Further on, we give examp...
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ISBN:
(纸本)9783642028939
We investigate sufficient conditions for a discrete nonlinear non-homogeneous dynamical system to converge to consensus. We formulate a theorem which is based on the notion of averaging maps. Further on, we give examples that demonstrate that the theory of convergence to consensus is still not complete.
Let M be a compact invariant set contained in a boundary hyperplane of the positive orthant of R-n for a discrete or continuous time dynamical system defined on the positive orthant. Using elementary arguments, we sho...
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ISBN:
(纸本)9783642028939
Let M be a compact invariant set contained in a boundary hyperplane of the positive orthant of R-n for a discrete or continuous time dynamical system defined on the positive orthant. Using elementary arguments, we show that M is uniformly weakly repelling in directions normal to the boundary in which M resides provided all normal Lyapunov exponents are positive. This result is useful in establishing uniform persistence of the dynamics.
A family of multi-point iterative methods for solving systems of nonlinear equations is described. Some classical methods are included in the mentioned family. Under certain conditions, convergence order is proved to ...
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ISBN:
(纸本)9783642028939
A family of multi-point iterative methods for solving systems of nonlinear equations is described. Some classical methods are included in the mentioned family. Under certain conditions, convergence order is proved to be 2d+1, where d is the order of the partial derivatives required to be zero in the solution. Moreover, different numerical tests confirm the theoretical results and allow us to compare these variants with Newton's method.
In this paper we review necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for switched linear positive systems. Both the state dependent and arbitrary switching cas...
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ISBN:
(纸本)9783642028939
In this paper we review necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for switched linear positive systems. Both the state dependent and arbitrary switching cases are considered and a number of applications are presented.
Positivity of states and parameters in dynamic models for chemical reaction networks are exploited by Chemical Reaction Network Theory (CRNT) to predict the potential for multistationarity of 'regular' network...
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ISBN:
(纸本)9783642028939
Positivity of states and parameters in dynamic models for chemical reaction networks are exploited by Chemical Reaction Network Theory (CRNT) to predict the potential for multistationarity of 'regular' networks without knowledge of parameter values. Especially for biochemical systems, however, CRNT's large application potential cannot be realized because most realistic networks are degenerate in the sense of CRNT. Here, we show how degenerate networks can be regularized such that the theorems and algorithms of CRNT apply. We employ the method in l case study for a bacterial reaction network of moderate size.
Positive linear systems display peculiar dynamics due to the positivity constraints on input, state and output variables. In this paper we review such peculiarities for externally and internally positive linear system...
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ISBN:
(纸本)9783642028939
Positive linear systems display peculiar dynamics due to the positivity constraints on input, state and output variables. In this paper we review such peculiarities for externally and internally positive linear systems. The properties of externally positive systems are shown in terms of poles and zeros location and input-output response, and those of internally positive systems in terms of eigenvalues location. Open problems are also presented. The presentation style of this paper is very informal, aiming to convey to the reader just a taste of the "importance of being positive".
The non-negativity of controls in positive linear discrete-time systems usually gives rise to complementarity conditions in the first-order Karush-Kuhn-Tucker optimality conditions - this complicates the analytic solu...
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ISBN:
(纸本)9783642028939
The non-negativity of controls in positive linear discrete-time systems usually gives rise to complementarity conditions in the first-order Karush-Kuhn-Tucker optimality conditions - this complicates the analytic solution and usually leads to numerical solutions. The intrinsic relationship between reachable sets anti the minimum-energy problem is exploited in this paper to obtain an analytic solution of the minimum-energy control problem for positive linear discrete-time systems with any pair of fixed terminal (initial and final) states.
We propose a model reduction method for positive systems that ensures the positivity of the reduced model. Our approach is based on constructing diagonal solutions of Lyapunov inequalities. These are linear matrix ine...
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ISBN:
(纸本)9783642028939
We propose a model reduction method for positive systems that ensures the positivity of the reduced model. Our approach is based on constructing diagonal solutions of Lyapunov inequalities. These are linear matrix inequalities (LMIs), which are shown to be feasible. Stability is preserved and an error bound in the H-infinity-norm is provided.
Robust control for Uncertain Networked control Systems with Random Delays addresses the problem of analysis and design of networked control systems when the communication delays are varying in a random fashion. The ra...
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ISBN:
(数字)9781848826786
ISBN:
(纸本)9781848826779
Robust control for Uncertain Networked control Systems with Random Delays addresses the problem of analysis and design of networked control systems when the communication delays are varying in a random fashion. The random nature of the time delays is typical for commercially used networks, such as a DeviceNet (which is a controller area network) and Ethernet network. The main technique used in this book is based on the Lyapunov-Razumikhin method, which results in delay-dependent controllers. The existence of such controllers and fault estimators are given in terms of the solvability of bilinear matrix inequalities. Iterative algorithms are proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. Finally, to demonstrate the effectiveness and advantages of the proposed design method in the book, numerical examples are given in each designed control system.
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