LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations

Ariadne Justi Bertolin; Ricardo C.L.F. Oliveira; Maurício C. de Oliveira; Pedro L.D. Peres

doi:10.1016/j.ifacol.2018.11.153

LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations

Ariadne Justi Bertolin, Ricardo C.L.F. Oliveira, Maurício C. de Oliveira, Pedro L.D. Peres

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Abstract

This paper revisits the problem of testing the robust stability of discrete-time linear systems with arbitrarily fast time-varying parameters, which includes the important class of switched discrete-time linear systems with arbitrary switching. By exploring the redundant description of the state space equations, sufficient linear matrix inequality (LMI) conditions of distinct complexities assuring robust stability are given in terms of the number k—1 of redundant equations. As k ≥ 1 increases, the conditions become also asymptotically necessary. Numerical examples borrowed from the literature illustrate that the proposed conditions can be computationally less demanding than other convergent relaxations.

Original language	English
Title of host publication	2nd IFAC Workshop on Linear Parameter Varying Systems LPVS 2018
Volume	51
Edition	26
DOIs	https://doi.org/10.1016/j.ifacol.2018.11.153
Publication status	Published - 23 Nov 2018
Externally published	Yes
Event	2nd IFAC Workshop on Linear Parameter Varying Systems - Florianopolis, Brazil Duration: 3 Sept 2018 → 5 Sept 2018

Conference

Conference	2nd IFAC Workshop on Linear Parameter Varying Systems
Country/Territory	Brazil
City	Florianopolis
Period	3/09/18 → 5/09/18

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10.1016/j.ifacol.2018.11.153

Cite this

LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations. / Justi Bertolin, Ariadne; Oliveira, Ricardo C.L.F.; de Oliveira, Maurício C. et al.
2nd IFAC Workshop on Linear Parameter Varying Systems LPVS 2018. Vol. 51 26. ed. 2018.

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Justi Bertolin, A, Oliveira, RCLF, de Oliveira, MC & Peres, PLD 2018, LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations. in 2nd IFAC Workshop on Linear Parameter Varying Systems LPVS 2018. 26 edn, vol. 51, 2nd IFAC Workshop on Linear Parameter Varying Systems, Florianopolis, Brazil, 3/09/18. https://doi.org/10.1016/j.ifacol.2018.11.153

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title = "LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations",

abstract = "This paper revisits the problem of testing the robust stability of discrete-time linear systems with arbitrarily fast time-varying parameters, which includes the important class of switched discrete-time linear systems with arbitrary switching. By exploring the redundant description of the state space equations, sufficient linear matrix inequality (LMI) conditions of distinct complexities assuring robust stability are given in terms of the number k—1 of redundant equations. As k ≥ 1 increases, the conditions become also asymptotically necessary. Numerical examples borrowed from the literature illustrate that the proposed conditions can be computationally less demanding than other convergent relaxations.",

author = "{Justi Bertolin}, Ariadne and Oliveira, {Ricardo C.L.F.} and {de Oliveira}, {Maur{\'i}cio C.} and Peres, {Pedro L.D.}",

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doi = "10.1016/j.ifacol.2018.11.153",

language = "English",

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AU - Justi Bertolin, Ariadne

AU - Oliveira, Ricardo C.L.F.

AU - de Oliveira, Maurício C.

AU - Peres, Pedro L.D.

PY - 2018/11/23

Y1 - 2018/11/23

N2 - This paper revisits the problem of testing the robust stability of discrete-time linear systems with arbitrarily fast time-varying parameters, which includes the important class of switched discrete-time linear systems with arbitrary switching. By exploring the redundant description of the state space equations, sufficient linear matrix inequality (LMI) conditions of distinct complexities assuring robust stability are given in terms of the number k—1 of redundant equations. As k ≥ 1 increases, the conditions become also asymptotically necessary. Numerical examples borrowed from the literature illustrate that the proposed conditions can be computationally less demanding than other convergent relaxations.

AB - This paper revisits the problem of testing the robust stability of discrete-time linear systems with arbitrarily fast time-varying parameters, which includes the important class of switched discrete-time linear systems with arbitrary switching. By exploring the redundant description of the state space equations, sufficient linear matrix inequality (LMI) conditions of distinct complexities assuring robust stability are given in terms of the number k—1 of redundant equations. As k ≥ 1 increases, the conditions become also asymptotically necessary. Numerical examples borrowed from the literature illustrate that the proposed conditions can be computationally less demanding than other convergent relaxations.

UR - http://dx.doi.org/10.1016/j.ifacol.2018.11.153

U2 - 10.1016/j.ifacol.2018.11.153

DO - 10.1016/j.ifacol.2018.11.153

M3 - Chapter in a published conference proceeding

VL - 51

BT - 2nd IFAC Workshop on Linear Parameter Varying Systems LPVS 2018

T2 - 2nd IFAC Workshop on Linear Parameter Varying Systems

Y2 - 3 September 2018 through 5 September 2018

ER -

LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations

Abstract

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