科学网关于指数稳定Exponential stable和渐进稳定Asymptotically stable

指数稳定是渐进稳定的一种指数稳定 expotential stable:v的导数小于负的e的多少次方乘以v推导出来,其收敛速度可描述
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指数稳定是渐进稳定的一种

指数稳定 expotential stable:v的导数小于负的e的多少次方乘以v推导出来,其收敛速度可描述

渐进稳定 asymptotically stable:v导数小于零即可,条件过于保守,可能出现收敛很慢的情况


关于指数式稳定exponentially stable:
In control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues (i.e., the poles of input-to-output systems) with strictly negative real parts. (i.e., in the left half of the complex plane).[1] A discrete-time input-to-output LTI system is exponentially stable if and only if the poles of its transfer function lie strictly within the unit circle centered on the origin of the complex plane. Exponential stability is a form of asymptotic stability. Systems that are not LTI are exponentially stable if their convergence is bounded by exponential decay.