Stability Analysis of Switched Linear Systems with Uncertainty and Delays

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Abstract

Combining the common quadratic Lyapunov functional approach and free-weighting matrix approach, this paper is devoted to the stability analysis of continuous-time switched linear systems (CTSLS) with uncertainty and time-delays. A particular class of matrix inequalities, the so-called Lyapunov–Metzler inequalities are introduced for the CTSLS to investigate the stability and performance in the presence of the uncertainty and delays. We provide sufficient conditions in terms of the Linear Matrix Inequality criterions to guarantee delay-dependent asymptotically stability under the uncertainty of the CTSLS. The combination of switching rule and switching output feedback controllers which will be designed to stabilize the CTSLS and satisfy a prespecified \({\mathcal{L}}_{2}\) gain performance. A example used jitterbug tools is provided to illustrate the effectiveness of the proposed method.

Keywords

CTSLS Lyapunov–Metzler inequalities Stability Jitterbug 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Electrical and Information EngineeringLanZhou University of TechnologyLanzhouChina

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