Autors: Perev, K. L.
Title: Gramians computation for hyperbolic distributed parameter systems
Keywords: distributed parameter system, hyperbolic partial differential equation, time-space separation, method of Fourier, vibrating string, controllability and observability gramians

Abstract: The paper considers the problem of gramians computation for linear hyperbolic distributed parameter systems. A special case of such systems is the vibrating string, which is described by wave partial differential equation. The weak solution of this equation is derived by applying the approach of time-space separation and using the Fourier method. This solution is transformed into a standard state space formulation by means of certain infinite dimensional matrices. The proposed system description is compared to a description based on a strongly continuous semigroup generated by a bounded system operator. Similarly to the finite dimensional case, it is shown that the derived weak solution consists of two parts. The zero input part is due to the initial conditions and participates in obtaining the observability gramian of the system. The zero state part is a consequence of the input signal effect and is used to compute the controllability gramian. The advantages of the presented approac



    IEEEXplore Proceedings of International Conference on Automatics and Informatics, pp. 24 – 29, 2021, Bulgaria, IEEEXplore

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