Absolute stability of general neutral Lurie indirect control systems with unbounded coefficients

doi:10.23952/jnfa.2017.35

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…It can also be pointed out that a wide class of existing results on non-linear stability and stabilization synthesis tools, c.f. [13,14,15,16,17,18], can be described in a unified manner under the hyperstablity and passivity theories, [19,20,21], which are more general. See also [22,23,24,25] and references therein for further theoretical and application work of stability, robust stability and hyperstability.…”

Section: Introductionmentioning

confidence: 99%

On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models

Sen

2019

IJERPH

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This paper studies the hyperstability and the asymptotic hyperstability of a single-input single-output controlled dynamic system whose feed-forward input-output dynamics is nonlinear and eventually time-varying consisting of a linear nominal part, a linear incremental perturbed part and a nonlinear and eventually time-varying one. The nominal linear part is described by a positive real transfer function while the linear perturbation is defined by a stable transfer function. The nonlinear and time-varying disturbance is, in general, unstructured but it is upper-bounded by the combination of three additive absolute terms depending on the input, output and input-output product, respectively. The non-linear time-varying feedback controller is any member belonging to a general class which satisfies an integral Popov’s-type inequality. This problem statement allows the study of the conditions guaranteeing the robust stability properties under a variety of the controllers designed for the controlled system and controller disturbances. In this way, set of robust hyperstability and asymptotic hyperstability of the closed-loop system are given based on the fact that the input-output energy of the feed-forward controlled system is positive and bounded for all time and any given initial conditions and controls satisfying Popov’s inequality. The importance of those hyperstability and asymptotic hyperstability properties rely on the fact that they are related to global closed-loop stability, or respectively, global closed-loop asymptotic stability of the same uncontrolled feed-forward dynamics subject to a great number of controllers under the only condition that that they satisfy such a Popov’s-type inequality. It is well-known the relevance of vaccination and treatment controls for Public Health Management at the levels of prevention and healing. Therefore, two application examples concerning the linearization of known epidemic models and their appropriate vaccination and/or treatment controls on the susceptible and infectious, respectively, are discussed in detail with the main objective in mind of being able of achieving a fast convergence of the state- trajectory solutions to the disease- free equilibrium points under a wide class of control laws under deviations of the equilibrium amounts of such populations.

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Section: Introductionmentioning

confidence: 99%

On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models

Sen

2019

IJERPH

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Absolute Stability of Neutral Systems with Lurie Type Nonlinearity

Diblı́k

Khusainov

Shatyrko

et al. 2021

Advances in Nonlinear Analysis

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The paper studies absolute stability of neutral differential nonlinear systems x ˙ ( t ) = A x t + B x t − τ + D x ˙ t − τ + b f ( σ ( t ) ) , σ ( t ) = c T x ( t ) , t ⩾ 0 $$ \begin{align}\dot x(t)=Ax\left ( t \right )+Bx\left ( {t-\tau} \right ) +D\dot x\left ( {t-\tau} \right ) +bf({\sigma (t)}),\,\, \sigma (t)=c^Tx(t), \,\, t\geqslant 0 \end{align} $$ where x is an unknown vector, A, B and D are constant matrices, b and c are column constant vectors, 𝜏 > 0 is a constant delay and f is a Lurie-type nonlinear function satisfying Lipschitz condition. Absolute stability is analyzed by a general Lyapunov-Krasovskii functional with the results compared with those previously known.

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Absolute stability of general neutral Lurie indirect control systems with unbounded coefficients

Cited by 2 publications

References 27 publications

On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models

On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models

Absolute Stability of Neutral Systems with Lurie Type Nonlinearity

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