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Positive systems constitute a class of systems that has the important property that its state variables are never negative, given a positive initial state. These systems appear frequently in practical applications, as these variables represent physical quantities, with positive sign (levels, heights, concentrations, etc.). It is also important to take this positivity into account for state observer design, as standard observers (for example Luenberger observers) might give illogical negative values.

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  • Positive systems (en)
  • 正向系統 (zh)
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  • 正向系統（Positive systems）是指一種系統，在給定正的初始值下，其狀態變數不會是負的。在一些實務應用中常會用到正向系統，因為這些變數表示實際的物理量，而這些物理量（如濃度、水位、高度等）不會為負值。 正向系統在控制系統的設計中相當重要。在狀態觀測器設計中也需考慮系統是否是正向系統，因為狀態觀測器可能會出現不合理的負值。 (zh)
  • Positive systems constitute a class of systems that has the important property that its state variables are never negative, given a positive initial state. These systems appear frequently in practical applications, as these variables represent physical quantities, with positive sign (levels, heights, concentrations, etc.). It is also important to take this positivity into account for state observer design, as standard observers (for example Luenberger observers) might give illogical negative values. (en)
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  • Positive systems constitute a class of systems that has the important property that its state variables are never negative, given a positive initial state. These systems appear frequently in practical applications, as these variables represent physical quantities, with positive sign (levels, heights, concentrations, etc.). The fact that a system is positive has important implications in the control system design. For instance, an asymptotically stable positive linear time-invariant system always admits a diagonal quadratic Lyapunov function, which makes these systems more numerical tractable in the context of Lyapunov analysis. It is also important to take this positivity into account for state observer design, as standard observers (for example Luenberger observers) might give illogical negative values. (en)
  • 正向系統（Positive systems）是指一種系統，在給定正的初始值下，其狀態變數不會是負的。在一些實務應用中常會用到正向系統，因為這些變數表示實際的物理量，而這些物理量（如濃度、水位、高度等）不會為負值。 正向系統在控制系統的設計中相當重要。在狀態觀測器設計中也需考慮系統是否是正向系統，因為狀態觀測器可能會出現不合理的負值。 (zh)
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