Abstract
The stability analysis is extremely important for open-loop and closed-loop systems. It is analysed in a general way for systems described by transfer functions, for feedback systems using transfer functions. Furthermore, it is developed for nonlinear systems. Several examples help its understanding.
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Notes
- 1.
The Euclidean norm of a vector is the square root of the sum of the squares of its elements, i.e. the “length” of a vector.
- 2.
The eigenvalues \(\lambda _i\) of a matrix \(\mathbf {A}\) are the roots of its characteristic polynomial of degree n, equal to the determinant of the matrix \(\mathbf {A} - \lambda \mathbf {I}\).
- 3.
A function \(f(\mathbf {x})\) is positive definite in a domain \(\mathscr {D}\) around the origin if f and its partial derivatives \(\partial f/\partial x_i\) exist and are continuous in \(\mathscr {D}\); if furthermore \(f(\mathbf {0})=0\), \(V(\mathbf {x})>0\) for \(x \ne 0\). It is semi-positive definite if \(V(\mathbf {x}) \ge 0\) for \(x \ne 0\).
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Corriou, JP. (2018). Stability Analysis. In: Process Control. Springer, Cham. https://doi.org/10.1007/978-3-319-61143-3_3
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DOI: https://doi.org/10.1007/978-3-319-61143-3_3
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