About: Input-to-state stability

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Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking, a control system is ISS if it is globally asymptotically stable in the absence of external inputs and if its trajectories are bounded by a function of the size of the input for all sufficiently large times.The importance of ISS is due to the fact that the concept has bridged the gap between and state-space methods, widely used within the control systems community.

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  • Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking, a control system is ISS if it is globally asymptotically stable in the absence of external inputs and if its trajectories are bounded by a function of the size of the input for all sufficiently large times.The importance of ISS is due to the fact that the concept has bridged the gap between and state-space methods, widely used within the control systems community. ISS unified the Lyapunov and input-output stability theories and revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, stability of nonlinear interconnected control systems, nonlinear detectability theory, and supervisory adaptive control. This made ISS the dominating stability paradigm in nonlinear control theory, with such diverse applications as robotics, mechatronics, systems biology, electrical and aerospace engineering, to name a few. The notion of ISS was introduced for systems described by ordinary differential equations by Eduardo Sontag in 1989. Since that the concept was successfully used for many other classes of control systems including systems governed by partial differential equations, retarded systems, hybrid systems, etc. (en)
  • 輸入-狀態穩定性（Input-to-state stability）簡稱ISS，是在有外部輸入時，非線性的控制理論中探討其穩定性的方式。簡單來說，控制系統具有輸入-狀態穩定性也就是指在沒有外在輸入時，系統會漸近穩定，而且在足夠長的時間後，系統軌跡會限制在和輸入大小有關的函數中。 輸入-狀態穩定性之所以重要，是因為此概念連接了輸入-輸出穩定性以及狀態空間法，這二個都是控制系統研究者常常使用的工具。輸入-狀態穩定性的標示方式是由在1989年開始使用。 (zh)
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  • 輸入-狀態穩定性（Input-to-state stability）簡稱ISS，是在有外部輸入時，非線性的控制理論中探討其穩定性的方式。簡單來說，控制系統具有輸入-狀態穩定性也就是指在沒有外在輸入時，系統會漸近穩定，而且在足夠長的時間後，系統軌跡會限制在和輸入大小有關的函數中。 輸入-狀態穩定性之所以重要，是因為此概念連接了輸入-輸出穩定性以及狀態空間法，這二個都是控制系統研究者常常使用的工具。輸入-狀態穩定性的標示方式是由在1989年開始使用。 (zh)
  • Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking, a control system is ISS if it is globally asymptotically stable in the absence of external inputs and if its trajectories are bounded by a function of the size of the input for all sufficiently large times.The importance of ISS is due to the fact that the concept has bridged the gap between and state-space methods, widely used within the control systems community. (en)
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  • Input-to-state stability (en)
  • 輸入-狀態穩定性 (zh)
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