This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen's and Wirtinger's inequalities, as well as the recently presented inequalities for single and double summation in [15]. The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.
Tumor volume modeling and control is a promising way to design more efficient, personalized tumor treatment. This requires a model of tumor growth dynamics, and a control law to design the therapy. Tumor growth models are usually nonlinear, while most control laws are linear, and the controllers are designed for approximate linear models thus stable operation is guaranteed only locally. We consider the application of a linear state feedback for a nonlinear tumor growth model, and carry out the qualitative analysis of the closed-loop model. We give conditions for the control law parameters to have a globally stable closed-loop system, and analyze the effect of the control law parameters on the steady-state tumor volume and the maximal drug injection.
The development of techniques for autonomous mobile robot navigation has been in focus for several decades [1,2]. The main objectives of this paper are twofold. One is to extend the potential based guiding (PBG) model to a more general form that can be approximated by a common type neuro-fuzzy algorithm. The extended model eliminates the strongly alternating behavior of PBG. The second is to propose a computation complexity reduction method for the general form of the neuro-fuzzy technique. Same examples are given to show the effectiveness of the extended guiding model.
Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special cases, both for the original models and the transformed ones.
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