Flow invariance in exploring stability for a class of nonlinear uncertain systems

Păstrăvanu, Octavian; Voicu, Mihail

doi:10.23919/ecc.2001.7076059

Cited by 3 publications

(10 citation statements)

References 7 publications

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“…Despite a rough similarity between the difference equation of DTNUS (1) and the differential equation describing the class of continuous-time systems considered in ( [3]), expecting strictly analogue properties for the solutions in the two cases is meaningless, as reflected by Remarks 1, 2, 5, 9. These remarks are able to outline the importance and the novelty of our study, because the discrete-time dynamics we are dealing with is not the result of uniformly sampling the continuous-time dynamics analyzed in ( [3]) (which would lead to a difference equation with unavoidable linear terms, generated by the first order approximation of the derivatives in the differential equation).…”

Section: Discussionmentioning

confidence: 99%

“…These remarks are able to outline the importance and the novelty of our study, because the discrete-time dynamics we are dealing with is not the result of uniformly sampling the continuous-time dynamics analyzed in ( [3]) (which would lead to a difference equation with unavoidable linear terms, generated by the first order approximation of the derivatives in the differential equation).…”

Section: Discussionmentioning

confidence: 99%

“…The class of nonlinear uncertain systems studied in the current paper may be roughly regarded as a discrete-time counterpart of the continuoustime dynamics discussed in ( [3]). In spite of the similarities occurring at the first glance between the mathematical description of the continuoustime and discrete-time cases, this deeper insight emphasizes noticeable differences, which are commented throughout the text.…”

Section: Introductionmentioning

confidence: 99%

“…Sections 3 and 4, by using the FI results, analyse CWAS, and respectively, CWEAS of the equilibrium point (EP) {O}. Some concluding remarks, including comparisons with the continuous-time case in ( [3]) are formulated in Section 5. Since the complete proofs of most results are laborious this version of the text limits them to some basic explanation.…”

Section: Introductionmentioning

confidence: 99%

“…This boundedness condition may be regarded as corresponding to the necessary condition in the continuous-time case, given by Theorem 6 in ( [3]). …”

mentioning

confidence: 99%

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Flow-Invariance Properties for a Class of Discrete-Time Nonlinear Uncertain Systems

Marinovici

Păstrăvanu

2003

Analysis and Optimization of Differential Systems

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The family of time-dependent rectangular sets, flow invariant with respect to a class of discrete-time nonlinear uncertain systems, is studied. The invariance results are further used for dealing with a special type of asymptotic stability, called componentwise asymptotic stability (CWAS), which can be characterized by difference inequalities. The particularisation of the CWAS conditions for exponential type timedependence yields the stronger property of componentwise exponential asymptotic stability (CWEAS), that is proven equivalent to some algebraic inequalities.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This boundedness condition may be regarded as corresponding to the necessary condition in the continuous-time case, given by Theorem 6 in ( [3]). …”

mentioning

confidence: 99%

See 3 more Smart Citations

Flow-Invariance Properties for a Class of Discrete-Time Nonlinear Uncertain Systems

Marinovici

Păstrăvanu

2003

Analysis and Optimization of Differential Systems

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Componentwise Asymptotic Stability Induced by Symmetrical Polyhedral Time-Dependent Constraints

Voicu

Păstrăvanu

2003

Analysis and Optimization of Differential Systems

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In this paper the concepts of componentwise asymptotic stability with respect to a differentiable vector function h( t) (approaching 0 as t -+ 00) (CWASh) and componentwise exponentially asymptotic stability (CWEAS), previously introduced, have been extended to Q-CWASh and Q-CWEAS (Q being a q x n real matrix), respectively, in order to cover the more general situation of polyhedral time-dependent fiowinvariant sets, defined by JQxJ :::; h(t), x E IR n , t E 1R+, symmetrical with respect to the equilibrium point of a given continuous-time linear systemwith the existence of a q x q matrix E such that EQ = QA, Eh(t) :::; h(t), where the bar operator C) transforms only the extra diagonal elements of E into their corresponding absolute values and does not change its diagonal elements. By specializing vector function h(t) in an exponentially decaying form, the concept of Q-CWEAS is characterized by the above mentioned matrix equation and an algebraic inequality. For Q = In these results consistently yield the earlier ones. As in this case, there exists a strong connection between Q-CWASh (Q-CWEAS) and the asymptotic stability, but now this connection is amended by the observability of the pair (Q, A).

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Flow-Invariance Method in Control — A Survey of Some Results

Voicu

Păstrăvanu

2004

Advances in Automatic Control

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Flow invariance in exploring stability for a class of nonlinear uncertain systems

Cited by 3 publications

References 7 publications

Flow-Invariance Properties for a Class of Discrete-Time Nonlinear Uncertain Systems

Flow-Invariance Properties for a Class of Discrete-Time Nonlinear Uncertain Systems

Componentwise Asymptotic Stability Induced by Symmetrical Polyhedral Time-Dependent Constraints

Flow-Invariance Method in Control — A Survey of Some Results

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