Prof. Michael Šebek: Robust aperiodicity

17.09.2009 - 10:00
Místo konání

Control systems with non-oscillating behavior are sometimes preferred or even required in particular applications. For systems with uncertainties, however, such a monotonic or aperiodic performance may or may not be robust. That is why not only robust stability, but also robust aperiodicity (monotonicity) has recently attracted attention of control theorists.
Robust aperiodicity of various kinds for families of polynomials with parametric uncertainties is treated in the lecture. For the case of a single parameter, an improved algorithm is presented to find maximum aperiodicity interval which is based on computing real zeros of certain polynomial matrices and polynomials.
For interval polynomials, a modified Kharitonov Theorem for aperiodicity is derived in a slightly simplified manner.
An original application of the Value Set concept is proposed along with a new concept of practical aperiodicity. Thanks to this, "aperiodic versions" of Zero Exclusion Condition and Edge Theorem are described which also make modifications of other important are possible. The results are implemented in the Polynomial Toolbox for Matlab which was employed to compute several illustrative examples that are presented.

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