L2 stability, H∞ control of switched homogeneous nonlinear systems and their semi‐tensor product of matrices representation. (14th January 2012)

• Record Type: Journal Article
• Authors: Zhang, Lijun; Zhang, Kuize
• Is Part Of: International journal of robust and nonlinear control. Volume 23:Number 6(2013)
• Page Start: 638
• Page End: 652
• Publication Date: 2012-01-14
• Subjects: Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.2781
• Languages: English
• ISSNs: 1049-8923

Abstract

<abstract abstract-type="main" id="rnc2781-abs-0001"> <title>SUMMARY</title> <p id="rnc2781-para-0002">This paper investigates the problems of <italic>L</italic>₂ stability and <italic>H</italic>_∞ control of switched homogeneous nonlinear systems. This paper gives that if a switched homogeneous nonlinear system with disturbance is internally homogeneously asymptotically stable, then it has a finite <italic>L</italic>₂ gain, and if a switched homogeneous nonlinear system with disturbance and controls is homogeneously stabilizable under the zero disturbance condition, its <italic>H</italic>_∞ control problem is solvable under some mild conditions, and a homogeneous solution is given. Then, via the semi‐tensor product of matrices method, the aforementioned obtained results are transformed to linear‐like forms, and the aforementioned obtained Hamilton–Jacobi–Isaacs inequality is transformed to a linear‐like matrix inequality, which makes it feasible to compute the solutions by computer. Copyright © 2012 John Wiley &amp; Sons, Ltd.</p> </abstract>