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Exponential Stability of Singularly Perturbed Systems

M. Corless, Luigi Glielmo

Open publisher page 20 citations

Abstract

In this paper we present some results and properties related to the exponential stability of singularly perturbed systems. Our main result is that, if both the reduced order system and the boundary-layer system are exponentially stable, then the full order system is exponentially stable and its rate of convergence approaches that of the reduced order system as the perturbation parameter approaches zero. Exponentially decaying norm bounds are given for the "slow" and "fast" components of the full order system trajectories.

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What this paper is about

In this paper we present some results and properties related to the exponential stability of singularly perturbed systems. Our main result is that, if both the reduced order system and the boundary-layer system are exponentially stable, then the full order system is exponentially stable and its rate of convergence approaches that of the reduced order system as the perturbation parameter approaches zero. Exponentially decaying norm bounds are given for the "slow" and "fast" components of the full order system trajectories.

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Available abstract

In this paper we present some results and properties related to the exponential stability of singularly perturbed systems. Our main result is that, if both the reduced order system and the boundary-layer system are exponentially stable, then the full order system is exponentially stable and its rate of convergence approaches that of the reduced order system as the perturbation parameter approaches zero. Exponentially decaying norm bounds are given for the "slow" and "fast" components of the full order system trajectories.

Key concepts: Exponential stability, Exponential growth, Singular perturbation, Exponential function, Perturbation (astronomy), Mathematics, Norm (philosophy), Convergence (economics)

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