Linear positive control systems on time scales; controllability
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In this paper, a necessary and sufficient condition for a linear system on a time scale to be positive is presented, and properties of positive reachable sets are investigated and characterizations of various controllability properties are presented.Abstract:
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear system on a time scale to be positive is presented. Properties of positive reachable sets are investigated and characterizations of various controllability properties are presented. A modified Gram matrix of the system is used to state necessary and sufficient condition of positive reachability of a positive system on an arbitrary time scale.read more
Citations
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Output controllability of the discrete-time linear switched systems
TL;DR: Three types of output controllability of discrete-time linear switched systems are discussed: from zero initial state to any final output, from anyInitial state to zero final output and from any initialState to anyfinal output.
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Exponential stability of nonlinear positive systems on time scales
TL;DR: In this article, it was shown that the positive uniform exponential stability of the linear approximation of a nonlinear system implies the positivity of the system, and that linearization preserves positivity.
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Pontryagin’s maximum principle for dynamic systems on time scales
TL;DR: In this article, an analogue of Pontryagin's maximum principle for dynamic equations on time scales is given, combining the continuous and the discrete Pontyagin maximum principles and extending them to other cases "in between".
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On consensus in the Cucker–Smale type model on isolated time scales
TL;DR: In this article, a consensus phenomenon in a Cucker-smale model where the magnitude of the step size is not necessarily a constant but it is a function of time is addressed.
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Local Positive Reachability of Nonlinear Continuous-Time Systems
TL;DR: It is shown that the system is locally positively reachable from the origin if and only if in some neighborhood of the origin, for each subface of the nonnegative cone of the state space there is a control value such that the vector field corresponding to this control value is tangent to the subface and nonzero.
References
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Book
Positive Linear Systems: Theory and Applications
Lorenzo Farina,Sergio Rinaldi +1 more
TL;DR: In this article, the authors define and define conditions of positivity of equilibria, including reachability and observability, and define a set of conditions for positive equilibrium. But they do not define the conditions of transparency.
Book
Positive 1D and 2D Systems
TL;DR: Elements of Probability Theory Uncertain Linear Systems and Robustness Linear Robust Control Design Some Limits of the Robusts Paradigm Probabilistic Methods for Robustity Monte Carlo Methods Randomized Algorithms in Systems and Control Probability Inequalities Statistical Learning Theory and Control Design Sequential Al algorithms for probabilistic Robust design SequentialAlgorithms for LPV Systems Scenario approach.