A polytopic approach for the nonlinear unknown input functional observers design: Application to a quadrotor aerial robots landing
Summary (1 min read)
Summary
- This paper considers a method of designing functional observers for continuous time nonlinear systems subject to unknown inputs.
- The proposed approach consists in rewriting the nonlinear model in a polytopic form (also known as multiple or Takagi-Sugeno models) applying the Sector Nonlinearity Transformation (SNT) and then apply the proposed algorithm for the observer design.
- Sufficient conditions for the asymptotic stability of the estimation error are given in terms of linear matrix inequalities (LMIs) and rank conditions.
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References
18,803 citations
"A polytopic approach for the nonlin..." refers background in this paper
...Originally introduced by [22], the T-S representation allows to exactly describe nonlinear systems, under the condition that the nonlinearities are bounded....
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3,183 citations
"A polytopic approach for the nonlin..." refers background or methods in this paper
...Note that several choices for the system (4) are possible (details on how to obtain (4) from (1) are detailed in [23])....
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...Proof: To prove this lemma, we need the following results: Lemma 4: [23] The continuous polytopic system ẋ(t) = M ∑...
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...This is reasonable since state variables as well as parameters of physical systems are bounded ( [4], [23] and the references therein)....
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...The polytopic Takagi-Sugeno (T-S) or Multiple Models (MM) decomposition is another appealing alternative solution to deal with nonlinear systems and to obtain the equivalent representation by a compact set of linear state space models with nonlinear weighting functions satisfying the convex sum property [23], [24], and [28]....
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...Herein, the well known sector nonlinearity transformation (SNT) may be used as a systematic and analytical method to rewrite and thus transform a nonlinear system into a polytopic T-S form without any loss of information [23] and [14]....
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2,544 citations
"A polytopic approach for the nonlin..." refers methods in this paper
...Thanks to the convexity of the weighting functions and to the linearity of the subsystems defining the vertices, some results can be established for nonlinear systems [7], [12], [17] using tools borrowed from the linear theory [18], [9]....
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2,402 citations
1,781 citations
"A polytopic approach for the nonlin..." refers background in this paper
...Observer design theory for nonlinear systems has been widely considered in the last decade and several contributions and theoretical approaches can be found in the literature (see for example [1], [11], [13], [16], [15])....
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