• International Journal of Control, Automation, and Systems
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• v.1 no.2
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• pp.171-177
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• 2003

In this paper, we investigate a robust $H_{\infty}$ state feedback control technique for continuous time bilinear systems with an additive disturbance input. The nonlinear robust $H_{\infty}$control for bilinear systems requires a solution to the state dependent algebraic Riccati equation (SDARE). We present a new robust $H_{\infty}$control technique based on the successive approximation method for solving the SDARE by converting bilinear systems into time-varying linear systems. The proposed control method guarantees robust stability for closed loop bilinear systems. The proposed algorithm is verified by numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.449-451
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• 2003

In this paper, the stability problem for singular bilinear system is investigated. We present state feedback control laws for two classes of singular bilinear plants. Asymptotic stability of the closed-loop systems is derived by employing singular Lyapunov's direct method. The primary advantage of our approach lies in its simplicity. In order to verify effectiveness of the results, two numerical examples are given.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.643-645
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• 1999

In between of linear and nonlinear systems lies a large class of bilinear systems. The major importance of bilinear systems lies in the applications to the real world systems such as many physical processes, many biological process, some economic process. Despite vast application of bilinear systems they have not been studied extensively in the domain of singularly perturbations except for a few minor results. In this paper we will utilize singular peturbations theory to obtain the closed-loop optimal solution for discrete-time bilinear systems.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2003.06a
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• pp.238-241
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• 2003

This paper presents a nonlinear least squares decision feedback equalizer Bilinear systems are attractive because of the ability to approximate a large class of nonlinear systems efficiently. The nonlinearity of channel is modeled using a bilinear system. The algorithms are derived by using the QR decomposition for minimization covariance matrix of prediction error by applying Givens rotation to the bilinear model. Result of computer simulation experiments that compare the performance of the bilinear DFE to two other DFE's in eliminating the intersymbol interference caused by a nonlinear channel are presented In the paper.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.17 no.5
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• pp.88-93
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• 2003

This paper presents a controller design method of bilinear systems via iterative method. The iterative procedure with auxiliary sequences is defined in the process of constructing coupled linear time varying systems from bilinear systems. To design the feedback controller for bilinear systems with quadratic cost function, an optimization procedure is given by the representation closely related to the Riccati approach. In the simulation results, it is shown that the suggested method accomplishes the improved performance and good convergence.

• Earthquakes and Structures
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• v.4 no.4
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• pp.397-428
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• 2013

This paper examines whether the "effective period" of bilinear isolation systems, as defined invariably in most current design codes, expresses in reality the period of vibration that appears in the horizontal axis of the design response spectrum. Starting with the free vibration response, the study proceeds with a comprehensive parametric analysis of the forced vibration response of a wide collection of bilinear isolation systems subjected to pulse and seismic excitations. The study employs Fourier and Wavelet analysis together with a powerful time domain identification method for linear systems known as the Prediction Error Method. When the response history of the bilinear system exhibits a coherent oscillatory trace with a narrow frequency band as in the case of free vibration or forced vibration response from most pulselike excitations, the paper shows that the "effective period" = $T_{eff}$ of the bilinear isolation system is a dependable estimate of its vibration period; nevertheless, the period associated with the second slope of the bilinear system = $T_2$ is an even better approximation regardless the value of the dimensionless strength,$Q/(K_2u_y)=1/{\alpha}-1$, of the system. As the frequency content of the excitation widens and the intensity of the acceleration response history fluctuates more randomly, the paper reveals that the computed vibration period of the systems exhibits appreciably scattering from the computed mean value. This suggests that for several earthquake excitations the mild nonlinearities of the bilinear isolation system dominate the response and the expectation of the design codes to identify a "linear" vibration period has a marginal engineering merit.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.689-696
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• 2006

This paper presents a new algorithm for the closed-loop $H_{\infty}$ composite control of weakly coupled bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation(SGA). By using weak coupling theory, the robust $H_{\infty}$ control can be obtained from two reduced-order robust $H_{\infty}$ control problems in parallel. The $H_{\infty}$ control theory guarantees robust closed-loop performance but the resulting problem is difficult to solve for uncertain bilinear systems. In order to overcome the difficulties inherent in the $H_{\infty}$ control problem, two $H_{\infty}$ control laws are constructed in terms of the approximated solution to two independent Hamilton-Jacobi-Isaac equations using the SGA method. One of the purposes of this paper is to design a closed-loop parallel robust $H_{\infty}$ control law for the weakly coupled bilinear systems with parameter uncertainties using the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.115-119
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• 1987

In this paper the observer design problem in bilinear systems is studied using the Walsh functions as approximating set of functions to find a finite series expansion of the state of bilinear system. A classical Liapnove method, to finding a class of observer feedback matrix, is applied to ensure uniform asymptotic stability of the observation error dynamics. An algorithm is derived for observer state eq. via Walsh function. The basic objective is to develop a computational algorithm for the determination of the coefficients in the expansion. This approach technique gives satisfactory result as well provides precise and effective method for the bilinear observer design problem.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.8
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• pp.384-391
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• 2001

This paper considers the problem of identifying the time-varying parameters of Bilinear systems. The Parameters, in this paper, are identified by using the EBPOMs(Extended Block Pulse Operational Matrices) which can reduce the burden of operation and the volume of error caused by matrices multiplication.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.4 no.5
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• pp.968-988
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• 2010

Anonymous hierarchical identity based encryption (HIBE) is an extension of identity based encryption (IBE) that can use an arbitrary string like an e-mail address for a public key, and it additionally provide the anonymity of identity in ciphertexts. Using the anonymous HIBE schemes, it is possible to construct anonymous communication systems and public key encryption with keyword search. This paper presents an anonymous HIBE scheme with constant size ciphertexts under prime order symmetric bilinear groups, and shows that it is secure under the selective security model. Previous anonymous HIBE schemes were constructed to have linear size ciphertexts, to use composite order bilinear groups, or to use asymmetric bilinear groups that is a special type of bilinear groups. Our construction is the first efficient anonymous HIBE scheme that has constant size ciphertexts and that uses prime order symmetric bilinear groups. Compared to the previous scheme of composite order bilinear groups, ours is ten times faster. To achieve our construction, we first devise a novel cancelable random blinding technique. The random blinding property of our technique provides the anonymity of our construction, and the cancellation property of our technique enables decryption.