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Stability Of Linear Delay Differential Equations by Dimitri Breda

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1Exponential Stability Of Linear Delay Impulsive Differential Equations

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For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions the equations is exponentially stable. We prove the same result for a delay differential equation $$ \dot{x}(t) + \sum_{i=1}^k A_i (t)x[h_i(t)] = f(t), $$ with impulses $$ x(\tau_i + 0) = B_i x(\tau_i - 0) $$ at fixed moments $\tau_i$. The proof is based on a solution representation formula obtained here.

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  • Title: ➤  Exponential Stability Of Linear Delay Impulsive Differential Equations
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 8.98 Mbs, the file-s for this book were downloaded 145 times, the file-s went public at Sat Sep 21 2013.

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2NECESSARY AND SUFFICIENT CONDITIONS OF ABSOLUTE ASYMPTOTIC STABILITY OF LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS WITH CONSTANT DELAY

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NECESSARY AND SUFFICIENT CONDITIONS ARE DETERMINED FOR THE ASYMPTOTIC STABILITY OF A TRIVIAL SOLUTION FOR LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS AND LINEAR EQUATIONS OF THE N-TH ORDER WITH ARBITRARY CONSTANT DELAY DELTA 0.

“NECESSARY AND SUFFICIENT CONDITIONS OF ABSOLUTE ASYMPTOTIC STABILITY OF LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS WITH CONSTANT DELAY” Metadata:

  • Title: ➤  NECESSARY AND SUFFICIENT CONDITIONS OF ABSOLUTE ASYMPTOTIC STABILITY OF LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS WITH CONSTANT DELAY
  • Authors:
  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 1.05 Mbs, the file-s for this book were downloaded 230 times, the file-s went public at Sun Jul 11 2010.

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