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This paper is devoted to the implications of the Kalman-Yakubovich-Popov Lemma, or Positive Real Lemma, when non-minimal state space realizations of transfer matrices of linear continuous systems are used. It is seen that some spurious parametrical conditions on the transfer matrix keep the Positive Real Lemma guaranteeing the stability from the associated Lyapunov equation.
In this paper, the discrete-time Kalman conjecture is shown to be false for systems of order two and above. Counterexamples are constructed. This contrasts with continuoustime domain systems where the Kalman conjecture is true for third-order systems.
In this paper, a feedback-based vaccination policy is designed for a SEIR epidemic model based on the concept of partial stability of the closed-loop system. The implementable vaccination rule is designed by only taking into account the subpopulations of exposed and infectious in contrast to previous approaches where the immune and susceptible subpopulations were also considered. Therefore, the current...
This paper proposes to use the concept of partial stability instead of that of global stability to analyze the dynamic behavior of epidemic models. The rationale behind this is that it is only needed, from a practical point of view, to ensure the boundedness of the infectious and infected subpopulations in order to get the disease under control. Thus, the partial stability of a controlled SEIR epidemic...
In this paper, the stability of a switched linear regular descriptor system is considered. It will be shown that if a certain simultaneous triangularization condition on the subsystems is fulfilled and all the subsystems are stable then the switched system is stable under arbitrary switching. The result involves different descriptor matrices and extends to the singular case well-known results from...
This paper studies the robust stability of uncertain internally delayed (i.e., in the state) systems being regulated by a sliding mode controller (SMC). A method for designing SMC is proposed. The robustness property and asymptotic stability of the system are discussed and sufficient conditions for the design of the switching hyperplane are given.
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