• Honam Mathematical Journal
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• v.45 no.1
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• pp.123-129
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• 2023

In this paper, we introduce the reverse of the operator Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for the Furuta inequality. More precisely, we prove that, if $A,\;B{\in}{\mathcal{B}}({\mathcal{H}})$ are self-adjoint operators with the spectra contained in the interval [m, M] with m < M and A ≤ B, then for any $r{\geq}{\frac{1}{t}}>1,\,t{\in}(0,\,1)$ $A^r{\leq}({\frac{M1_{\mathcal{H}}-A}{M-m}}m^{rt}+{\frac{A-m1_{\mathcal{H}}}{M-m}}M^{rt}){^{\frac{1}{t}}}{\leq}K(m,\;M,\;r)B^r,$ where K (m, M, r) is the generalized Kantorovich constant.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.6
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• pp.547-553
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• 2006

This paper studies digital control of biodynamic model of HIV-1 via intelligent digital redesign (IDR). The purpose of the IDR is to develop an equivalent digital fuzzy controller maintaining the satisfactory performance of an existing continuous-time fuzzy controller in the sense of the state-matching. Some conditions for the stability as well as the global state-matching are provided.. They are given by the form of the linear matrix inequalities (LMIs) and thereby easily tractable by the convex optimization techniques. The main features of the proposed method are that 1) the generalized control scheme is provided for the multirate as well as the single-rate digital controllers; 2) a new compensated block-pulse function method is applied to closely match the states of the continuous-time and the sampled-data fuzzy systems in the discrete-time domain; 3) the two-step procedure of IDR is presented to prevent the performance degradation caused by the additional stability conditions. The applicability of the proposed approach is shown through the biodynamic model of HIV-1.