• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.621-637
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• 2005

A hybrid method solving regularized structured linear total least norm (RSTLN) problems, which have highly ill-conditioned coefficient matrix with special structures, is suggested and analyzed. This scheme combining RSTLN algorithm and separation by parts guarantees the convergence of parameters and has an advantages in reducing the residual norm and relative error of solutions. Computational tests for problems arisen in signal processing and image formation process confirm that the presenting method is effective for more accurate solutions to (R)STLN problem than the (R)STLN algorithm.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.373-385
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• 2006

To solve a class of nonlinear parameter estimation problems, a method combining the regularized structured nonlinear total least norm (RSNTLN) method and parameter separation scheme is suggested. The method guarantees the convergence of parameters and has an advantages in reducing the residual norm over the use of RSNTLN only. Numerical experiments for two models appeared in signal processing show that the suggested method is more effective in obtaining solution and parameter with minimum residual norm.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.151-164
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• 2005

The regularized structured total least norm (RSTLN) method finds an approximate solution x and error matrix E to the overdetermined linear system (H + E)x $\approx$ b, preserving structure of H. A new separation scheme by parts of variables for the regularized structured total least norm on blind deconvolution problem is suggested. A method combining the regularized structured total least norm method with a separation by parts of variables can be obtain a better approximated solution and a smaller residual. Computational results for the practical problem with Block Toeplitz with Toeplitz Block structure show the new method ensures more efficiency on image restoration.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.489-504
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• 2008

In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial $H_2$ norm of modes, which serves as a measure of the intensity of modes to system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible tructures with piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by imultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.