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Stability Analysis of Interconnected Systems With “Mixed” Negative-Imaginary and Small-Gain Properties

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2 Author(s)
Patra, S. ; Control Syst. Centre, Univ. of Manchester, Manchester, UK ; Lanzon, A.

In this letter, an analytical framework is proposed to examine stability of two stable, linear time invariant systems interconnected in positive feedback where the systems have “mixed” properties of negative-imaginary and small-gain. Using the notion of dissipativity, the interconnection of systems is guaranteed to be finite-gain stable under the condition that the dc loop gain is contractive. This work builds on Griggs, and exploits a new set of frequency dependent triplets that was introduced in above reference to “mix” two unconditional stability statements, i.e., small-gain and passivity. Unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative-imaginary systems are connected in a feedback loop can be “mixed” with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop. The usefulness of the proposed analytical framework is demonstrated via a numerical example.

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Automatic Control, IEEE Transactions on  (Volume:56 ,  Issue: 6 )