Control of multiplicative noise stochastic gene regulation systems by the attractive ellipsoid technique

Lozada‐Castillo, Norma; Poznyak, Alexander S.; Chairez, Isaac

doi:10.1007/s12555-013-0226-2

Cited by 2 publications

(1 citation statement)

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“…where φ : R n × R m → R n and g : R n → R p are a suitable right-hand side, and the parameter u(t) is chosen from a control set U ⊂ R m of admissible control functions of type u(x) such that the closedloop system has a well-defined solution, and have been objects of the theory of ODEs for a long time (Lozada-Castillo et al, 2014;Poznyak et al, 2014a,b;Poznyak, 2015). We consider previous references to review stages of AEM.…”

Section: Aemmentioning

confidence: 99%

An implicit class of continuous dynamical system with data-sample outputs: a robust approach

Juárez

Azhmyakov

Espinoza

et al. 2019

IMA Journal of Mathematical Control and Information

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This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.

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Section: Aemmentioning

confidence: 99%