1990 | John Doyle, Bruce Francis, Allen Tannenbaum
The chapter introduces the fundamental concepts and norms used in the analysis and design of control systems. It begins by defining norms for signals, including the 1-norm, 2-norm, and ∞-norm, and discusses power signals and their properties. The chapter then extends these norms to systems, introducing the 2-norm and ∞-norm for transfer functions. It provides tables summarizing input-output norm relationships, which are useful for predicting the effect of disturbances on system outputs. The chapter also covers input-output relationships, providing tables that relate the norms of inputs and outputs for different types of signals. Finally, it includes optional sections on power analysis and the autocorrelation function, which are essential for understanding the statistical properties of signals and their impact on system performance.The chapter introduces the fundamental concepts and norms used in the analysis and design of control systems. It begins by defining norms for signals, including the 1-norm, 2-norm, and ∞-norm, and discusses power signals and their properties. The chapter then extends these norms to systems, introducing the 2-norm and ∞-norm for transfer functions. It provides tables summarizing input-output norm relationships, which are useful for predicting the effect of disturbances on system outputs. The chapter also covers input-output relationships, providing tables that relate the norms of inputs and outputs for different types of signals. Finally, it includes optional sections on power analysis and the autocorrelation function, which are essential for understanding the statistical properties of signals and their impact on system performance.