A multivariable extension of the Tsypkin criterion using a Lyapunov-function approach

Vikram Kapila; Wassim M. Haddad

doi:10.1109/9.481622

A multivariable extension of the Tsypkin criterion using a Lyapunov-function approach

Vikram Kapila, Wassim M. Haddad

Mechanical and Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

For analyzing the stability of discrete-time systems containing a feedback nonlinearity, the Tsypkin criterion is the closest analog to the Popov criterion which is used for analyzing such systems in continuous time. Traditionally, the proof of this criterion is based upon input-output properties and function analytic methods. In this paper we extend the Tsypkin criterion to multivariable systems containing an arbitrary number of monotonic sector-bounded memoryless time-invariant nonlinearities, along with providing a Lyapunov function proof for this classical result.

Original language	English (US)
Pages (from-to)	149-152
Number of pages	4
Journal	IEEE Transactions on Automatic Control
Volume	41
Issue number	1
DOIs	https://doi.org/10.1109/9.481622
State	Published - 1996

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/9.481622

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abstract = "For analyzing the stability of discrete-time systems containing a feedback nonlinearity, the Tsypkin criterion is the closest analog to the Popov criterion which is used for analyzing such systems in continuous time. Traditionally, the proof of this criterion is based upon input-output properties and function analytic methods. In this paper we extend the Tsypkin criterion to multivariable systems containing an arbitrary number of monotonic sector-bounded memoryless time-invariant nonlinearities, along with providing a Lyapunov function proof for this classical result.",

author = "Vikram Kapila and Haddad, {Wassim M.}",

note = "Funding Information: That is, instead of finding the condition for the state variables z(k) to approach the zero equilibrium point, sufficient conditions for z(k+ 1) and y(k) to approach zero are found. Obviously, if the system is observable artd z(k t 1) and y(k) approach zero, the system arrives Manuscript received October 26, 1993; revised June 28, 1994, July 26, 1994, and Marlch 10, 1995. This work was supported in part by the National Science Foundation under Grants ECS-9 109558 and ECS-9496249. The authors are with the School of AerospaceE ngineering, Georgia Institute of Technology, Atlanta, GA 30332-0150 USA. Publisher Item Identifier S 0018-9286(96)00395-9.",

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N1 - Funding Information: That is, instead of finding the condition for the state variables z(k) to approach the zero equilibrium point, sufficient conditions for z(k+ 1) and y(k) to approach zero are found. Obviously, if the system is observable artd z(k t 1) and y(k) approach zero, the system arrives Manuscript received October 26, 1993; revised June 28, 1994, July 26, 1994, and Marlch 10, 1995. This work was supported in part by the National Science Foundation under Grants ECS-9 109558 and ECS-9496249. The authors are with the School of AerospaceE ngineering, Georgia Institute of Technology, Atlanta, GA 30332-0150 USA. Publisher Item Identifier S 0018-9286(96)00395-9.

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A multivariable extension of the Tsypkin criterion using a Lyapunov-function approach

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