# TOPOLOGICAL SYNTHESIS OF SELECTIV INVARIANT AUTOMATIC CONTROL SYSTEMS

The paper discusses various ways of achieving the property of selective invariance (disturbance attenuation or rejection) for automatic control systems with arbitrary causal structure. We consider linear time-invariant models of the topological, structural and parametric levels of certainty. An arc in the signal flow graph whose transfer function has zeros or poles equal to the disturbance spectrum provides the zero steady-state reaction of the system. Topological formula for the graph’s transfer function, transformed to a polynomial form, allows obtaining localization conditions for the internal environment model placement. Since the requirements of invariance and stability contradict one another, the problem is to decompose the invariant control systems synthesis procedure. An illustrative example of the stabilization of an invariant system in the frequency domain is given.

**Authors:** D. H. Imaev, M. Yu. Shestopalov , S. V. Kvashnin

**Direction:** Informatics, Computer Technologies And Control

**Keywords:** Control system, topology, structure, signal flow graph, selective invariance, disturbance, spectrum, synthesis

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