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What is exponential stability?
Exponential stability is mainly used in measuring discrete-time system, state bounds and stability domains. The measuring figure is obtained by evolving the vector norm of Lyapunov function. However, systems that are not LTI are considered exponentially stable because here the convergence is bounded by anexponential decay.
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What are the two systems of exponential stability?
There are two systems of exponential stability— one is linearsystem, and the other is non-linear system. For alinear system, sufficient conditions are given asymptotic stability and thereby, exponential bounds are derived.
On the other hand, for non-linear systems, sufficient conditions for exponential stability yield a stability domain. The applications in this domain are demonstrated in observer design for thediscrete-time nonlinear system.
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An example of exponential stability and linear system:
Here, in this graph, the graph on the right side shows impulse response of two systems. The green curve shows impulse response , while the blue curve shows system . Both these equations are oscillatory and return to original value of 0.
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