Abstract
Lyapunov theory, one of the most successfully and widely used tools, provides a means of determining stability without explicit knowledge of system solutions. Many remarkable results [1,2,3,4] have been presented for flexible systems based on Lyapunov’s direct method. Barrier Lyapunov function is a novel concept that can be employed to deal with control problems with output constraints [5,6,7]. In [5], a barrier Lyapunov function is employed for control of SISO nonlinear systems with an output constraint. A novel asymmetric time-varying barrier Lyapunov function is used in [7] to ensure the time-varying output constraint satisfaction for strict feedback nonlinear systems. In the neural control field, two challenging and open problems are addressed in [6] by using a barrier Lyapunov function in the presence of unknown functions. However, in all the papers mentioned above, barrier Lyapunov functions are designed for linear or nonlinear ODE systems. There is little information about how to handle the constraints for PDEs and there is a need to explore an effective method for the control of flexible systems with constraint problems.
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He, W., Liu, J. (2019). Vibration Control of a Flexible Beam with Output Constraint. In: Active Vibration Control and Stability Analysis of Flexible Beam Systems. Springer, Singapore. https://doi.org/10.1007/978-981-10-7539-1_4
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DOI: https://doi.org/10.1007/978-981-10-7539-1_4
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