Article

# Stabilisation and improvement of performance by extension of universal formula in the presence of disturbance

Dept. of Electr. & Comput. Eng., Tehran Univ., Iran

IEE Proceedings - Control Theory and Applications (Impact Factor: 1.05). 04/2005; DOI: 10.1049/ip-cta:20041128 Source: IEEE Xplore

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**ABSTRACT:**It is shown that any stabilizing, certainty equivalence control used within an adaptive control system, causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimatorâ€™s output error ep, for every frozen value of the index or parameter vector p upon which both the estimator and controller dynamics depend. The fact that certainty equivalence implies detectability has been known for some time â€“ this has been shown to be so whenever the process model is linear and the controller and estimator models are also linear for every frozen value of p. In this paper, use is made of recently introduced concepts of input-to-state stability and detectability for nonlinear systems to prove that the same implication is valid in a more general, nonlinear setting.Systems & Control Letters 01/1998; · 1.67 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Lemma 5 in [2] was incorrect. A correction is provided here. The error does not a#ect the rest of the results in the paper. 1 The Error and the Fix There is an error in the statement and the proof of Lemma 5 in the paper [2]. The estimate about # 0 (|z(t)|) towards the end of the proof of Lemma 5 is incorrect. It should be replaced by #(|d(s)|)#(z(s)) ds. Without knowing whether #(|z(s)|) is bounded, one cannot conclude that # 0 (|z(t)|) is bounded. Below we provide a correction of the lemma by posing a boundedness condition on the function #.09/2002; - [Show abstract] [Hide abstract]

**ABSTRACT:**For linear systems, it is known that there exists a state observer if and only if the system is detectable, or in other words, asymptotically stabilizable by output injection. In this paper, it is shown that asymptotic stabilizability by output injections is neither necessary nor sufficient for the construction of a nonlinear observer which may not have an exponential error decay rate. The concept of uniform observers is introduced and necessary conditions and sufficient conditions are given for the construction of uniform observers.Systems & Control Letters. 01/1999;

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