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In this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles. [ABSTRACT FROM AUTHOR]

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate nonexpansive or contractive self-mappings from initial conditions to points of the state-trajectory solution. The existence of a unique fixed point leading to a globally asymptotically stable equilibrium point is investigated, in particular, under easily testable sufficiency-type stability conditions. The study is performed for both the uncontrolled case and the controlled case under a wide class of state feedback laws. [ABSTRACT FROM AUTHOR]

Robust stability results for nominally linear hybrid systems are obtained from total stability theorems for purely continuous-time and discrete-time systems by using the powerful tool of fixed point theory. The class of hybrid systems dealt consists, in general, of coupled continuous-time and digital systems subject to state perturbations whose nominal (i.e., unperturbed) parts are linear and, in general, time-varying. The obtained sufficient conditions on robust stability under a wide class of harmless perturbations are dependent on the values of the parameters defining the overbounding functions of those perturbations. The weakness of the coupling dynamics in terms of norm among the analog and digital substates of the whole dynamic system guarantees the total stability provided that the corresponding uncoupled nominal subsystems are both exponentially stable. Fixed point stability theory is used for the proofs of stability. A generalization of that result is given for the case that sampling is not uniform. The boundedness of the state-trajectory solution at sampling instants guarantees the global boundedness of the solutions for all time. The existence of a fixed point for the sampled state-trajectory solution at sampling instants guarantees the existence of a fixed point of an extended auxiliary discrete system and the existence of a global asymptotic attractor of the solutions which is either a fixed point or a limit n globally stable asymptotic oscillation. [ABSTRACT FROM AUTHOR]

In recent literature concerning fixed point theory for self-mappings T : X → X in metric spaces (X, d), there are some new concepts which can be mutually related so that the inherent properties of each one might be combined for such self-mappings. Self-mappings T : X → X can be referred to, for instance, as Kannan-mappings, reasonable expansive mappings, and Picard T-stable mappings. Some relations between such concepts subject either to sufficient, necessary, or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations. [ABSTRACT FROM AUTHOR]

A generalization of Halpern's iteration is investigated on a compact convex subset of a smooth Banach space. The modified iteration process consists of a combination of a viscosity term, an external sequence, and a continuous nondecreasing function of a distance of points of an external sequence, which is not necessarily related to the solution of Halpern's iteration, a contractive mapping, and a nonexpansive one. The sum of the real coefficient sequences of four of the above terms is not required to be unity at each sample but it is assumed to converge asymptotically to unity. Halpern's iteration solution is proven to converge strongly to a unique fixed point of the asymptotically nonexpansive mapping. [ABSTRACT FROM AUTHOR]

The article discusses the nonegativity and positivity concepts and associated attributes for the state and output trajectory results of active linear time-invariant systems depicted by functional differential equations subject to point time delays. It is suggested that the respective nonnegativities and positivities introduced hierarchically from the weakest to the strongest while distinguishing the matching properties when used to the state space or to the output space including the zero-initial state or zero-input responses.

The importance of positive real transfer functions relies on the fact that they are associated with positive linear systems. Those systems possess the property that their input-output product time-integral, which is a measure of the total enerty, is nonnegative. Such a property can be also formulated in the discrete context. It is shown that a discrete positive real transfer function is obtained from a positive real continuous one of relative order zero being strictly stable poles via discretization by a sampler and zero-order hold device provided that the direct input-output transmission gain is sufficiently large. It is also proved that a discrete positive real transfer function may be obtained from a stable continuous one of relative order zero and high direct input-output gain which posses simple complex conjugate critically stable poles even in the case that this one is not positive real. For that purpose, the use of an appropriate phase-lag or phase lead compensating network for the continuous transfer function may be required to ensure positive realness of the discrete transfer function. [ABSTRACT FROM AUTHOR]

This paper deals with the identification of linear time—varying continuous—time systems whose parameters have bounded first-order time-derivative under square-integrable output noise. The proposed parameter updating algorithm is one of σ-modification type with Covariance Matrix. The Covariance Matrix updating rule is performed by using a modification with respect to standard previous estimation schemes used for time-invariant plants. Such a modification consists of including, apart from the standard ones in least-squares estimation with forgetting factor, two extra additive weighted terms involving the identity matrix as well as the second power of such a matrix with the appropriate signs. That parameter estimation strategy ensures that the norm of the covariance matrix is always finitely upper-bounded without using adaptation freezing techniques over a prescribed norm threshold. The main role played by the σ-modification relies on introducing a penalty for large values of the covariance inverse and the parametrical error. Furthermore, in the most general formalism setting, the knowledge of absolute upper-bounds on either the parameter vector or its time-derivative are not requested. The estimation scheme guarantees the asymptotic convergence of the prediction error to zero and that of the estimates to the true parameters under standard properties of persistent excitation of the input and controllability of both plant and filter realizations in the case when the plant is noise-free and either time-invariant after finite time asymptotically time-invariant. If the plant is slowly time-varying and the covariance matrix is updated with the standard least-squares rule, the variations of the integrals of the squares of the estimation vector and its time-derivative norms vary not faster than uniformly linearly with the interval lengths considered for integration. Furthermore, the overall changes are arbitrarily small over any finite time-interval provided that the time-derivative of the true parameter vector and the correction coefficients in the covariance updating rule are arbitrarily small. [ABSTRACT FROM AUTHOR]

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance. [ABSTRACT FROM AUTHOR]

Some trapezoid and mid-point type inequalities related to the Hermite–Hadamard inequality on the disk of center C = (a , b) and radius R, D (C , R) ⊆ R 2 , are investigated. It is shown that the estimated value obtained in the trapezoid and mid-point type inequalities has a relation with the integral of the partial derivative of the considered function on ∂ (C , R) , the boundary of D (C , R) . [ABSTRACT FROM AUTHOR]

This paper presents a multicontroller structure for an SEIADR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-dead lying bodies recovered by immunity, or immune, subpopulations) epidemic model, which has three different controls involving feedback, namely, the vaccination on the susceptible subpopulation, the antiviral treatment on the symptomatic infectious subpopulation, and the impulsive removal on the infective lying bodies. The incorporation of the asymptomatic infectious and infective dead bodies to SEIR-type models allows a better modeling of diseases where the death bodies are infective as, for instance, the Ebola disease. The proposed supervised multicontroller scheme consists of a parallel disposal of several alternative controller parameterizations together with a switching scheme that chooses the active controller through consecutive time intervals via a supervisory decision scheme. The supervisory scheme decides to switch or not at testing time instants. Switching is performed to a distinct active scheme to the current active if the tentative controller minimizes the value of a loss function compared to the values of the other control schemes available in the parallel controller disposal. The supervisory loss (or cost) function incorporates several additive weighted terms including the infection loss function evolution and the vaccination, antiviral treatment, and bodies removal efforts. [ABSTRACT FROM AUTHOR]

This paper deals with some new theorems and inequalities about a Fejér type integral inequality which estimate the difference between the right and middle part in Fejér inequality with new bounds. Also some applications to higher moments of random variables, an error estimate for trapezoidal formula, and some inequalities in connection with special means are given. [ABSTRACT FROM AUTHOR]