Stability analysis of negative imaginary systems with real parametric uncertainty – the single-input single-output case

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Stability analysis of negative imaginary systems with real parametric uncertainty – the single-input single-output case

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Real parametric uncertainty is common in many applications. In this study, the authors analyse the robust stability of feedback loops of single-input single-output systems with negative imaginary frequency response subject to real parametric uncertainty. A recent result on the stability of such feedback loops is specialised to this case, resulting in a very simple stability condition dependent only on the steady-state parameters of the systems. The structured singular value for this system type is also obtained, and it is shown that it yields related but more constrained, easily computable stability guarantees. In a numerical example, the robust stability of a control loop for a DC machine subject to real parametric uncertainty is analysed.

Inspec keywords: robust control; state feedback; uncertain systems

Other keywords: stability analysis; single-input single-output case; DC machine; negative imaginary systems; steady state parameters; feedback loops; real parametric uncertainty; negative imaginary frequency response; robust stability

Subjects: Stability in control theory

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