On stabilization of linear systems with stochastic disturbances and input saturation

Antonie Arij Stoorvogel; Siep Weiland; Ali Saberi

On stabilization of linear systems with stochastic disturbances and input saturation

Antonie Arij Stoorvogel, Siep Weiland, Ali Saberi

Research output: Contribution to conference › Paper › peer-review

10 Citations (Scopus)

152 Downloads (Pure)

Abstract

It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in Lp then also the state will be in Lp. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication is no longer directly applicable. Several people have studied the effect of external inputs in Lp either directly or in the context of ISS as introduced by Sontag. In this paper we will study the effect of external stochastic disturbances on linear systems with input saturation and we establish that when we can achieve internal global asymptotic stability then we can also achieve a bounded variance for the state.

Original language	Undefined
Pages	3007-3012
Number of pages	6
Publication status	Published - Dec 2004
Event	43rd IEEE Conference on Decision and Control, CDC 2004 - The Atlantis, Paradise Island, Bahamas Duration: 14 Dec 2004 → 17 Dec 2004 Conference number: 43

Conference

Conference	43rd IEEE Conference on Decision and Control, CDC 2004
Abbreviated title	CDC
Country/Territory	Bahamas
City	Paradise Island
Period	14/12/04 → 17/12/04

Keywords

EWI-16657
IR-69072

Access to Document

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1428925&isnumber=30837

Cite this

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title = "On stabilization of linear systems with stochastic disturbances and input saturation",

abstract = "It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in Lp then also the state will be in Lp. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication is no longer directly applicable. Several people have studied the effect of external inputs in Lp either directly or in the context of ISS as introduced by Sontag. In this paper we will study the effect of external stochastic disturbances on linear systems with input saturation and we establish that when we can achieve internal global asymptotic stability then we can also achieve a bounded variance for the state.",

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year = "2004",

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note = "43rd IEEE Conference on Decision and Control, CDC 2004 ; Conference date: 14-12-2004 Through 17-12-2004",

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T1 - On stabilization of linear systems with stochastic disturbances and input saturation

AU - Stoorvogel, Antonie Arij

AU - Weiland, Siep

AU - Saberi, Ali

N1 - Conference code: 43

PY - 2004/12

Y1 - 2004/12

N2 - It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in Lp then also the state will be in Lp. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication is no longer directly applicable. Several people have studied the effect of external inputs in Lp either directly or in the context of ISS as introduced by Sontag. In this paper we will study the effect of external stochastic disturbances on linear systems with input saturation and we establish that when we can achieve internal global asymptotic stability then we can also achieve a bounded variance for the state.

AB - It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in Lp then also the state will be in Lp. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication is no longer directly applicable. Several people have studied the effect of external inputs in Lp either directly or in the context of ISS as introduced by Sontag. In this paper we will study the effect of external stochastic disturbances on linear systems with input saturation and we establish that when we can achieve internal global asymptotic stability then we can also achieve a bounded variance for the state.

KW - EWI-16657

KW - IR-69072

M3 - Paper

SP - 3007

EP - 3012

T2 - 43rd IEEE Conference on Decision and Control, CDC 2004

Y2 - 14 December 2004 through 17 December 2004

ER -