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Observability and controllability analysis for sandwich systems with backlash

Luo N., Tan Y., Dong R.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 4

803--814

In this paper, an approach to analyze the observability and controllability of sandwich systems with backlash is proposed. In this method, a non-smooth state-space function is used to describe the sandwich systems with backlash which are also non-smooth non-linear systems. Then, a linearization method based on non-smooth optimization is proposed to derive a linearized state-space function to approximate the non-smooth sandwich systems within a bounded region around the equilibrium point that we are interested in. Afterwards, both observability and controllability matrices are constructed and the methods to analyze the observability as well as controllability of sandwich system with backlash are derived. Finally, numerical examples are presented to validate the proposed method.

A sample time assign for a discrete interval parabolic system with the two-dimensional uncertain parameter space

Mitkowski W., Oprzędkiewicz K.

Systems Science

2004

Vol. 30, no 1

43-50

In this paper, the sample time assign problem for a class of uncertain parameter discrete parabolic systems is presented. The system under consideration is described by the discrete abstract state space equation in the Hubert space. The system's uncertainty is described by the two-dimensional vector containing uncertain parameters of a heat equation. The type of the system uncertainty implies that the state operator and the control operator for the discussed system are interval operators. As a measure of the system's uncertainty the weighted mean of widths of interval state equation coefficients and the Euclidean norm of the both widths were accepted. The proposed performance indices allows us to calculate a range of sample time that guarantees that the required maximal permissible system's uncertainty is not exceeded after a system's discretization. The results are depicted by an example.