<abstract xmlns="http://www.w3.org/1999/xhtml"> We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.</abstract>

We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.

Quadratic Performance Analysis of Switched Affine Time–Varying Systems

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Quadratic Performance Analysis of Switched Affine Time\u2013Varying Systems"}

We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and...

Quadratic Performance Analysis of Switched Affine Time–Varying Systems

Published Online: Oct 03, 2018

Page range: 429 - 440

Received: Aug 08, 2017

Accepted: Apr 21, 2018

DOI: https://doi.org/10.2478/amcs-2018-0032

Keywords
switched affine systems, time-varying systems, quadratic stabilization, tracking, L2 gain, switching law, differential LMIs, observers

© 2018 Wenzhi Li, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Quadratic Performance Analysis of Switched Affine Time–Varying Systems

Published Online: Oct 03, 2018

Page range: 429 - 440

Received: Aug 08, 2017

Accepted: Apr 21, 2018

DOI: https://doi.org/10.2478/amcs-2018-0032

Keywordsswitched affine systems, time-varying systems, quadratic stabilization, tracking, L2 gain, switching law, differential LMIs, observers

© 2018 Wenzhi Li, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
switched affine systems, time-varying systems, quadratic stabilization, tracking, L2 gain, switching law, differential LMIs, observers