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Article

Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback

by *,† and
Laboratory of Mathematical Control Theory, Udmurt State University, 426034 Izhevsk, Russia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(5), 853; https://doi.org/10.3390/math8050853
Received: 6 May 2020 / Revised: 21 May 2020 / Accepted: 22 May 2020 / Published: 24 May 2020
We consider a control system defined by a linear time-varying differential equation of n-th order with uncertain bounded coefficients. The problem of exponential stabilization of the system with an arbitrary given decay rate by linear static state or output feedback with constant gain coefficients is studied. We prove that every system is exponentially stabilizable with any pregiven decay rate by linear time-invariant static state feedback. The proof is based on the Levin’s theorem on sufficient conditions for absolute non-oscillatory stability of solutions to a linear differential equation. We obtain sufficient conditions of exponential stabilization with any pregiven decay rate for a linear differential equation with uncertain bounded coefficients by linear time-invariant static output feedback. Illustrative examples are considered. View Full-Text
Keywords: linear differential equation; exponential stability; linear output feedback; stabilization; uncertain system linear differential equation; exponential stability; linear output feedback; stabilization; uncertain system
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MDPI and ACS Style

Zaitsev, V.; Kim, I. Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback. Mathematics 2020, 8, 853. https://doi.org/10.3390/math8050853

AMA Style

Zaitsev V, Kim I. Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback. Mathematics. 2020; 8(5):853. https://doi.org/10.3390/math8050853

Chicago/Turabian Style

Zaitsev, Vasilii, and Inna Kim. 2020. "Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback" Mathematics 8, no. 5: 853. https://doi.org/10.3390/math8050853

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