$l_{2}-l_{\infty}$ Model Reduction for Switched LPV Systems With Average Dwell Time

Abstract

In this note, the model reduction problem for a class of discrete-time switched linear parameter varying systems under average dwell time switching is investigated. A parameterized reduced-model is constructed and the corresponding existence conditions of such models are derived via strict LMI formulation. The minimal average dwell time among all the subsystems and the desired reduced system are obtained such that the resulting model error system is exponentially stable and has a guaranteed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> error performance. A numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results.