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Recall the definition of a dynamic, finite dimensional, time invariant system, in both continuous and discrete time. .
Recall the definition of stability according to Lyapunov, in both continuous and discrete time. Moreover, state which element this property belongs to, according to the mathematical structure of the system. .
State when an equilibrium is isolated. .
Recall the definition of region of attraction. .
Recall the linearisation method and its drawbacks. .
What is the phase plane? Depending on the position of the eigenvalues on the Gauss-Argand plane, illustrate all possible trajectories for a linear system. How is it used in case of a nonlinear one? .
Consider a scalar function V(x), continuous with its first derivatives (C^1). Define all possible properties that it might have locally, and express the condition which makes them global. .
Consider the values of x such that V(x)=V_bar, where V_bar is a positive value. What do they define? .
State the Lyapunov theorem and try to prove it for both continuous and discrete time systems. .
State the Krasowski-La Salle theorem. .
State the necessary and sufficient condition for the asymptotic stability in linear systems. .
What is the backstepping method? When and how is it used? .
Recall the small gain theorem for both SISO and MIMO systems. .
State the circle criterion. .
Talk about control synthesis in SISO systems and make a comparison with the MIMO ones. .
Recall the formal definition of poles and zeros for MIMO systems. .
State the blocking property of zeros and explain its meaning in a MIMO context. .
Created by: Filotì
 

 



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