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The growing stringency of fuel economy, emissions, and drivability requirements has led to proliferation of powertrain systems that have multiple discrete operating modes. Systematic approaches to the development of optimal and robust control systems for such powertrains are needed to contain their increased development times and costs. In this paper, we propose a new approach for controlling switched systems that is applicable to powertrain systems with multiple operating modes. Our approach reduces the complexity of computing a control law to a linear programming problem defined over a finite number of states in each operating mode. The methodology is designed to be suitable for practical applications while, under appropriate conditions, providing near-optimal performance. An application to the direct injection stratified charge engine with two distinct operating modes is given to illustrate our approach.