, 1) is weakly detectable, then the system 2 : g(r,h(x),u) is an observer for (6.1), namely 0 e IP is asymptotically stable with respect to the error system è : f (x,u) -g(r -e,h(r, According to Definition 6.1, if uniformly on r and u
, We now start by stating the results given by Vidyasagar in [8a1. We consider the nonlinear system described by (6.1) and the following hypotheses
0) : 0, furthermore, there exist positive constants c1 and c2 such that for all r and u llV,/(", r)ll S ct ,
, 1) and the assumptions (?ll) and, (712) pertaini,ng to it. If we can fi,nd a teedback control u: l@) such that (i,) 1 is conti, Theorem 6.L Suppose system
ii) n -0 fs a uni,fonnly asymptotically stable equilibri'um point of ù: T(x,z(u) ,
, 1) is weakly detectable, then n:0 and z:0 is a uni,formly asymptoti ,cally stable equili,brium point of the system ù: f@,te), p.2
, Proof : See Vidyasagar
, Tsinias ha^s relaxed condition (i) in Vidyasagar's theorem, and only considered 7(c) to be continuous
, 1) is wealcly detectable and i:: f (a,l@D is (locally) asurnptotically stable at 0 e W then the output feedbacle u:',tk) asymptotically stabilizes ù: f@,te)), 2 -eQ,h(x),tQD, Theorem 6.2 If system, p.64
, Chapitrc 7. Conclusions and future work
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