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Applying control-theoretic approaches to capacity provisioning and performance management of Web servers is gaining increasing popularity in the past several years. This paper presents a novel control-theoretic approach that is a combination of linear-parameter-varying (LPV) techniques and workload characterization using alpha-stable-model based stochastic envelopes. In particular, we parameterize a control-oriented Web-server model and resulting controller using scheduling variables that are workload-distribution parameters. By further applying an alpha-stable modeling technique to identify the load parameters and using them to online schedule the LPV model and controller, the presented solutions not only allow the system to adapt to load variations, but also show great promise in handling self-similar workloads. The proposed framework is applied to a Web-server CPU management problem, where the server CPU frequencies are dynamically tuned and implemented via the dynamic voltage scaling mechanism to achieve the target response time. Simulations using real Web-server traces are conducted to show the strength of the proposed approach.