The first important contribution of this paper is to introduce for the first time a duality-based interpretation of piecewise affine (PWA) systems. This enables PWA controller synthesis to be formulated as a convex optimization problem. PWA L{sub}2-gain analysis and synthesis is also extended to PWA systems whose output is also a PWA function of the state (as opposed to a piecewise-linear function). In addition, a convex optimization program is proposed to compute a PWA differential inclusion for nonlinear systems for which the nonlinearity is a function of one variable. A numerical example illustrates the usefulness of the new approach.
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机译：本文的第一个重要贡献是首次介绍分段仿射（PWA）系统的基于二元的解释。这使得PWA控制器综合能够被配制为凸优化问题。 PWA L {Sub} 2-GAIN分析和合成也扩展到PWA系统，其输出也是状态的PWA函数（与分段线性函数相反）。另外，建议计算凸优化程序以计算非线性系统的非线性系统的PWA差分夹杂物，其中非线性是一个变量的函数。数值示例说明了新方法的有用性。
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