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# Lect_31 - Nonlinear Systems and Control Lecture 31...

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Unformatted text preview: Nonlinear Systems and Control Lecture # 31 Stabilization Output Feedback – p. 1/1 2 In general, output feedback stabilization requires the use of observers. In this lecture we deal with three simple cases where an observer is not needed Minimum Phase Relative Degree One Systems Passive systems System with Passive maps from the input to the derivative of the output – p. 2/1 2 Minimum Phase Relative Degree One Systems ˙ x = f ( x ) + g ( x ) u, y = h ( x ) f (0) = 0 , h (0) = 0 , L g h ( x ) negationslash = 0 , ∀ x ∈ D Normal Form: φ (0) = 0 , L g φ ( x ) = 0 , bracketleftBigg η y bracketrightBigg = bracketleftBigg φ h ( x ) bracketrightBigg ˙ η = f ( η, y ) , ˙ y = γ ( x )[ u − α ( x )] , γ ( x ) negationslash = 0 – p. 3/1 2 Assumptions: The origin of ˙ η = f ( η, 0) is exponentially stable c 1 bardbl η bardbl 2 ≤ V 1 ( η ) ≤ c 2 bardbl η bardbl 2 ∂V 1 ∂η f ( η, 0) ≤ − c 3 bardbl η bardbl 2 vextendsingle vextendsingle vextendsingle vextendsingle...
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