International Symposium on Nonlinear Theory and its Applications
Stability of a Switched System for Continuous-time Tomographic Image Reconstruction
Omar M. Abou Al-Ola, Ken’ichi Fujimoto, Tetsuya Yoshinaga,
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We have presented a novel approach for reconstructing tomographic images consisting of a continuous-time image reconstruction (CIR)system described by differential equations for solving ill-posed inverse problems. We see that a switched system with a piecewise smooth vector field, which describes a block CIR system, can reconstruct better images than the smooth CIR system. For investigating an essential property of the switched system, we considered a small system and gave its analytic solution. In this paper, we give a common Lyapunov function for the family of all subsystems to prove the stability of the switched system.