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There has been increasing research effort in applying control-theoretic approaches to performance management for computer systems such as Web servers, database systems, and storage systems. Since today's Internet servers and applications are often operated under dynamically changing load conditions, linear control designs may not suffice to provide desired performance guarantees. This paper presents a linear-parameter-varying (LPV) approach to the modeling and performance control of Web servers in order to achieve performance-based service level agreement (SLA). In particular, admission control for Web servers is used as a case study. By applying system identification to empirical data, an LPV system is developed to approximate the dynamics of Web server admission control from rejection ratio to response time, where the time-varying workload parameters are chosen as scheduling variables. An LPV robust control is then designed to meet response time SLA. The performance of the LPV control is compared with that of a linear design. By exploring the nature of dependence of server performance on time-varying load and operating conditions, the proposed general framework are applicable to a diverse spectrum of server-based applications. The utilization of scheduling parameters can be generalized to accommodate more sophisticated workload characterization and complicated server environments.