Abstract
This paper studies the general output observation problem for linear infinite-dimensional control systems with bounded input and output operators. Both, the plant and the observer are described by state space models with linear, unbounded system operators, generating strongly continuous semigroups. The plant has two inputs and two outputs. One input is for control, available to the observer, and the other for disturbance. In turn, one output is for the so-called measured signal, available to the observer, and the other for the so-called output to be observed. Using knowledge of the control and the measured output the observer output is to asymptotically follow the output to be observed and that condition is called the output observation. Disturbances are generated by a homogeneous, linear system with an unknown initial condition. Some sufficient conditions for the output observation are derived. These conditions involve the plant, observer and disturbance system operators and consist of two linear operator equations with one of them being an algebraic Sylvester equation. We show that the obtained conditions are constructive and under the assumption on the exponential detectability of the plant allow to derive a design procedure for the output observer. The presented results extend those for linear finite-dimensional control systems.
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Emirsajłow, Z. (2021). Output Observers for Linear Infinite-Dimensional Control Systems. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Automatic Control, Robotics, and Information Processing. Studies in Systems, Decision and Control, vol 296. Springer, Cham. https://doi.org/10.1007/978-3-030-48587-0_3
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