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The concept of stability introduced in the famous thesis of Aleksandr Lyapunov [1] is one of the central notions of the modern systems and control theory. Many problems of state estimation and control can be reduced to a stability analysis or to a stabilization problemStabilization problem. This chapter surveys some elements of the Lyapunov theory and its generalizations such as finite-time stabilityFinite-time stability (FTS) [2], fixed-time stabilityFixed-time stability (FxTS) [3] and input-to-state stabilityInput-to-state stability (ISS) [4].

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Stability and Robustness

  • 章节

  • 发表日期：

    2025年

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  • Andrey Polyakov

摘要

The concept of stability introduced in the famous thesis of Aleksandr Lyapunov [1] is one of the central notions of the modern systems and control theory. Many problems of state estimation and control can be reduced to a stability analysis or to a stabilization problemStabilization problem. This chapter surveys some elements of the Lyapunov theory and its generalizations such as finite-time stabilityFinite-time stability (FTS) [2], fixed-time stabilityFixed-time stability (FxTS) [3] and input-to-state stabilityInput-to-state stability (ISS) [4].