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RESEARCH PRODUCT
On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems
Alireza KhayatianNavid NorooziHamid Reza KarimiSaeed Ahmadizadehsubject
Lyapunov functionsmall-gain conditions0209 industrial biotechnologyInterconnectionStability (learning theory)Computer Science Applications1707 Computer Vision and Pattern Recognition02 engineering and technologyState (functional analysis)Computer Science ApplicationsWhole systems0-global asymptotic stabilityTheoretical Computer Scienceinput-to-state stabilitysymbols.namesakeparameterised discrete-time systems020901 industrial engineering & automationDiscrete time and continuous timeControl theoryControl and Systems Engineering0202 electrical engineering electronic engineering information engineeringsymbols020201 artificial intelligence & image processing0-global asymptotic stability; input-to-state stability; integral input-to-state stability; parameterised discrete-time systems; small-gain conditions; Control and Systems Engineering; Theoretical Computer Science; Computer Science Applications1707 Computer Vision and Pattern Recognitionintegral input-to-state stabilityMathematicsdescription
This paper addresses integral input-to-state stability iISS for a feedback interconnection of parameterised discrete-time systems involving two subsystems. Particularly, we give a construction for a smooth iISS Lyapunov function for the whole system from the sum of nonlinearly weighted Lyapunov functions of individual subsystems. Motivations for such a construction are given. We consider two main cases. The first one investigates iISS for the whole system when both subsystems are iISS. The second one gives iISS for the interconnected system when one of subsystems is allowed to be input-to-state stable. The approach is also valid for both discrete-time cascades and a feedback interconnection of iISS and static systems. Examples are given to illustrate the effectiveness of the results.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-08-30 |