### Abstract

Original language | American English |
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Pages | 2973-2974 |

Number of pages | 2675 |

State | Published - 1 Jan 1993 |

Externally published | Yes |

Event | American Control Conference - Duration: 1 Jan 1993 → … |

### Conference

Conference | American Control Conference |
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Period | 1/01/93 → … |

### Fingerprint

### Cite this

*Note on a change of coordinates for nonlinear SISO systems with singular points*. 2973-2974. Paper presented at American Control Conference, .

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**Note on a change of coordinates for nonlinear SISO systems with singular points.** / Retchkiman, Zvi.

Research output: Contribution to conference › Paper › Research

TY - CONF

T1 - Note on a change of coordinates for nonlinear SISO systems with singular points

AU - Retchkiman, Zvi

PY - 1993/1/1

Y1 - 1993/1/1

N2 - In the paper titled `Asymptotic Output Tracking Through Singular Points for a class of Uncertain SISO Nonlinear Systems', a transformation T:Rn×R+→Rn+β which takes (x,t)qq(Z,ζ,Φ) defined by Z1 = h(x) Z2 = Lfh(x)qqZα = Lfα-1h(x) ζα+1 = a0(x)+b0(x)u ζα+2 = a1(x,u)+b0(x)u′+b1(x,u)u ζα+3 = a2(x,u,u′)+b2(x,u,u′)u+2b1(x,u)u′+ b0( x)u″qqζα+β = aβ-1(x,u,qq,u(β-2))+bβ-1(x,u, qq,u( β-2))u+qq+b0(x)u(β-1) {Φi(x)}i = α+1n was proposed in order to get rid of the singularity and being able to compute an admissible control u. There was also discussed that T was formed by at least n linearly independent functions as long as x≠xs i.e., no singular points, (this was assumed when x = xs). The main purpose of this paper is to present a proof where it is shown that T given by (1) provides us with a set of at least n linearly independent functions in case of having singular points.

AB - In the paper titled `Asymptotic Output Tracking Through Singular Points for a class of Uncertain SISO Nonlinear Systems', a transformation T:Rn×R+→Rn+β which takes (x,t)qq(Z,ζ,Φ) defined by Z1 = h(x) Z2 = Lfh(x)qqZα = Lfα-1h(x) ζα+1 = a0(x)+b0(x)u ζα+2 = a1(x,u)+b0(x)u′+b1(x,u)u ζα+3 = a2(x,u,u′)+b2(x,u,u′)u+2b1(x,u)u′+ b0( x)u″qqζα+β = aβ-1(x,u,qq,u(β-2))+bβ-1(x,u, qq,u( β-2))u+qq+b0(x)u(β-1) {Φi(x)}i = α+1n was proposed in order to get rid of the singularity and being able to compute an admissible control u. There was also discussed that T was formed by at least n linearly independent functions as long as x≠xs i.e., no singular points, (this was assumed when x = xs). The main purpose of this paper is to present a proof where it is shown that T given by (1) provides us with a set of at least n linearly independent functions in case of having singular points.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=0027335102&origin=inward

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M3 - Paper

SP - 2973

EP - 2974

ER -