Robust observer design by sign-stability for the monitoring of population systems

López, Isaac José Pérez; Puertas, María Luz; Rodríguez, Carmelo; Gámez, Manuel; Varga, Zoltán

doi:10.1016/j.jfranklin.2019.01.023

Cited by 4 publications

(2 citation statements)

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“…In Figure 4, it is shown how the solution of observer (11) with an initial value z(0)= [(18, 15,9] T approaches the solution of the original system, with an initial value x(0) = [10, 6, 5] T , considered as the "unknown solution" of (6).…”

Section: Remarkmentioning

confidence: 99%

“…A review paper on the different applications of MST in population biology was authored by Varga [8], and somewhat more recent surveys were published by Gámez [9] and Varga et al [10]. In López et al's work [11], by applying a technique of signed digraphs, a new, general approach to the design of a robust observer in continuous-time Lotka-Volterra models was proposed.…”

Section: Introductionmentioning

confidence: 99%

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Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment

et al. 2022

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This paper is a contribution to the modeling–methodological development of the application of mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model is considered, where both the reproduction and survival rates decrease as the total population size increases. In this context, the monitoring problem means that, from the observation of the size of certain age classes as a function of time, we want to recover (estimate) the whole state process (i.e., the time-dependent size of the rest of the classes). First, for the linearization approach, conditions for the existence and asymptotic stability of a positive equilibrium are obtained, then the discrete-time observer design method is applied to estimate an unknown state trajectory near the equilibrium, where we could observe a single age class. It is also shown how the observer design can be used to detect an unknown change in the environment that affects the population dynamics. The environmental change is supposed to be generated by additional dynamics (exosystem). Now, the Leslie-type model is extended with this exosystem, and the observer design is applied to this extended system. In this way, an estimation can be obtained for different (constant or periodic) environmental changes as well.

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Section: Remarkmentioning

confidence: 99%