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

作者：Patra Sourav^*; Lanzon Alexander

来源：IEEE Transactions on Automatic Control, 2011, 56(6): 1395-1400.

DOI：10.1109/TAC.2011.2122670

• Bounded-real system
• dissipativeness
• finite-gain stability
• interconnected system
• negative-imaginary system
• positive feedback

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, et al. [14] 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.

• 出版日期2011-6