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1

Construction of algebraic and difference equations with a prescribed solution space

Moysis L., Karampetakis N. P.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 1

19--32

EN

This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ) β (k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ) . This work deals with the inverse problem of constructing a family of polynomial matrices A(σ) such that the system A(σ) β (k) = 0 satisfies some given forward and backward behavior. Initially, the connection between the backward behavior of an AR representation and the forward behavior of its dual system is showcased. This result is used to construct a system satisfying a certain backward behavior. By combining this result with the method provided by Gohberg et al. (2009) for constructing a system with a forward behavior, an algorithm is proposed for computing a system satisfying the prescribed forward and backward behavior.

2

An improvement in stable Pade approximation using constrained minimization

Bandyopadhyay B., Singare P. S.

Systems Science

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2006

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Vol. 32, no 2

5-17

EN

In this paper, an improvement in Pade approximation is proposed to reduce the order of a linear-time-invariant higher order stable system, using the Hermite-Biehler stability theorem. Two free parameters are introduced in the denominator polynomial of the reduced model. It will be shown that for any positive values of these two parameters, the resulting reduced model will be stable. The numerator polynomial and these two parameters are obtained by matching time moments. In this proposed algorithm, the reduced model matches (r + 2) time moments exactly while (r + 3)-th moment is matched approximately. The proposed method is illustrated by two numerical examples.

3

Design of output feedback compensator for smart structure model via reduced order model

Umapathy M., Bandyopadhyay B., Unbehauen H.

Systems Science

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2002

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Vol. 28, nr 4

61-84

EN

A method of designing an output feedback compensator for vibration control of a flexible smart cantilever beam based on its reduced order model is presented. By retaining the first two vibration modes the state space model is obtained from a smart structure Finite Element Model (FEM). A reduced order model is obtained by retaining the first vibration mode. It has been shown that an output feedback compensator can be obtained for the smart structure model from the state feedback gains designed from its reduced order model. It has also been shown that if the compensator is placed in the closed loop with the higher order system, it guarantees the closed loop stability. As the states are not needed for feedback, the method is simple and can be easily implemented.