Energy approach to stability analysis of the linear stationary dynamic systems
A new approach was proposed to analyze the stability of the linear continuous stationary dynamic systems. It is based on the decomposition of a square H 2 norm of the transfer function of the dynamic system into parts corresponding either to particular eigenvalues of the system matrix, or to pairwis...
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| Veröffentlicht in: | Automation and remote control 2016-12, Vol.77 (12), p.2132-2149 |
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| container_title | Automation and remote control |
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| creator | Yadykin, I. B. Iskakov, A. B. |
| description | A new approach was proposed to analyze the stability of the linear continuous stationary dynamic systems. It is based on the decomposition of a square H
2
norm of the transfer function of the dynamic system into parts corresponding either to particular eigenvalues of the system matrix, or to pairwise combinations of these eigenvalues. The spectral decompositions of a square H
2
norm of the transfer function with multiple poles were obtained using the residues of the transfer function and their derivatives. Exact analytical expressions for calculation of the quadratic forms of the corresponding expansions were derived for an arbitrary location of the eigenvalues in the left half-plane. The obtained decompositions allow one to characterize the contribution of individual eigen-components or their pairwise combinations into the asymptotic variation of the system energy. We propose the energy criterion for estimation of the system stability margins that uses an evaluation of energy accumulated in a group of weakly stable system modes. This approach is illustrated by calculating the energy of a band-pass filter. |
| doi_str_mv | 10.1134/S0005117916120043 |
| format | Article |
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2
norm of the transfer function of the dynamic system into parts corresponding either to particular eigenvalues of the system matrix, or to pairwise combinations of these eigenvalues. The spectral decompositions of a square H
2
norm of the transfer function with multiple poles were obtained using the residues of the transfer function and their derivatives. Exact analytical expressions for calculation of the quadratic forms of the corresponding expansions were derived for an arbitrary location of the eigenvalues in the left half-plane. The obtained decompositions allow one to characterize the contribution of individual eigen-components or their pairwise combinations into the asymptotic variation of the system energy. We propose the energy criterion for estimation of the system stability margins that uses an evaluation of energy accumulated in a group of weakly stable system modes. This approach is illustrated by calculating the energy of a band-pass filter.</description><identifier>ISSN: 0005-1179</identifier><identifier>EISSN: 1608-3032</identifier><identifier>DOI: 10.1134/S0005117916120043</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Bandpass filters ; CAE) and Design ; Calculus of Variations and Optimal Control; Optimization ; Computer-Aided Engineering (CAD ; Control ; Decomposition ; Dynamic stability ; Dynamical systems ; Dynamics ; Eigenvalues ; Linear Systems ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Mechanical Engineering ; Mechatronics ; Quadratic forms ; Robotics ; Stability analysis ; Systems analysis ; Systems stability ; Systems Theory ; Transfer functions</subject><ispartof>Automation and remote control, 2016-12, Vol.77 (12), p.2132-2149</ispartof><rights>Pleiades Publishing, Ltd. 2016</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-d026e3e1d55436a9b9872cec4100a84a36b8d3b5e9b1c047c848e72e18efed4e3</citedby><cites>FETCH-LOGICAL-c349t-d026e3e1d55436a9b9872cec4100a84a36b8d3b5e9b1c047c848e72e18efed4e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0005117916120043$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0005117916120043$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Yadykin, I. B.</creatorcontrib><creatorcontrib>Iskakov, A. B.</creatorcontrib><title>Energy approach to stability analysis of the linear stationary dynamic systems</title><title>Automation and remote control</title><addtitle>Autom Remote Control</addtitle><description>A new approach was proposed to analyze the stability of the linear continuous stationary dynamic systems. It is based on the decomposition of a square H
2
norm of the transfer function of the dynamic system into parts corresponding either to particular eigenvalues of the system matrix, or to pairwise combinations of these eigenvalues. The spectral decompositions of a square H
2
norm of the transfer function with multiple poles were obtained using the residues of the transfer function and their derivatives. Exact analytical expressions for calculation of the quadratic forms of the corresponding expansions were derived for an arbitrary location of the eigenvalues in the left half-plane. The obtained decompositions allow one to characterize the contribution of individual eigen-components or their pairwise combinations into the asymptotic variation of the system energy. We propose the energy criterion for estimation of the system stability margins that uses an evaluation of energy accumulated in a group of weakly stable system modes. This approach is illustrated by calculating the energy of a band-pass filter.</description><subject>Bandpass filters</subject><subject>CAE) and Design</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Computer-Aided Engineering (CAD</subject><subject>Control</subject><subject>Decomposition</subject><subject>Dynamic stability</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Eigenvalues</subject><subject>Linear Systems</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mechanical Engineering</subject><subject>Mechatronics</subject><subject>Quadratic forms</subject><subject>Robotics</subject><subject>Stability analysis</subject><subject>Systems analysis</subject><subject>Systems stability</subject><subject>Systems Theory</subject><subject>Transfer functions</subject><issn>0005-1179</issn><issn>1608-3032</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kM1LxDAQxYMouFb_AG8BL16qM03apkdZ1g8QPajnkqbT3Sz9WJPsof-9LetBFE8DM7_3mPcYu0S4QRTy9g0AUsS8wAwTACmO2AIzULEAkRyzxXyO5_spO_N-C4AIiViwl1VPbj1yvdu5QZsNDwP3QVe2tWHa9rodvfV8aHjYEG9tT9rNQLBDr93I67HXnTXcjz5Q58_ZSaNbTxffM2If96v35WP8_PrwtLx7jo2QRYhrSDIShHWaSpHpoipUnhgyEgG0klpklapFlVJRoQGZGyUV5QmhooZqSSJi1wff6evPPflQdtYbalvd07D3JapCTFXM9hG7-oVuh72bgs2UAoXpDEcMD5Rxg_eOmnLnbDclLBHKueHyT8OTJjlo_MT2a3I_nP8VfQHEyHyz</recordid><startdate>20161201</startdate><enddate>20161201</enddate><creator>Yadykin, I. B.</creator><creator>Iskakov, A. B.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20161201</creationdate><title>Energy approach to stability analysis of the linear stationary dynamic systems</title><author>Yadykin, I. B. ; Iskakov, A. B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c349t-d026e3e1d55436a9b9872cec4100a84a36b8d3b5e9b1c047c848e72e18efed4e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Bandpass filters</topic><topic>CAE) and Design</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Computer-Aided Engineering (CAD</topic><topic>Control</topic><topic>Decomposition</topic><topic>Dynamic stability</topic><topic>Dynamical systems</topic><topic>Dynamics</topic><topic>Eigenvalues</topic><topic>Linear Systems</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mechanical Engineering</topic><topic>Mechatronics</topic><topic>Quadratic forms</topic><topic>Robotics</topic><topic>Stability analysis</topic><topic>Systems analysis</topic><topic>Systems stability</topic><topic>Systems Theory</topic><topic>Transfer functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yadykin, I. B.</creatorcontrib><creatorcontrib>Iskakov, A. B.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Automation and remote control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yadykin, I. B.</au><au>Iskakov, A. B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Energy approach to stability analysis of the linear stationary dynamic systems</atitle><jtitle>Automation and remote control</jtitle><stitle>Autom Remote Control</stitle><date>2016-12-01</date><risdate>2016</risdate><volume>77</volume><issue>12</issue><spage>2132</spage><epage>2149</epage><pages>2132-2149</pages><issn>0005-1179</issn><eissn>1608-3032</eissn><abstract>A new approach was proposed to analyze the stability of the linear continuous stationary dynamic systems. It is based on the decomposition of a square H
2
norm of the transfer function of the dynamic system into parts corresponding either to particular eigenvalues of the system matrix, or to pairwise combinations of these eigenvalues. The spectral decompositions of a square H
2
norm of the transfer function with multiple poles were obtained using the residues of the transfer function and their derivatives. Exact analytical expressions for calculation of the quadratic forms of the corresponding expansions were derived for an arbitrary location of the eigenvalues in the left half-plane. The obtained decompositions allow one to characterize the contribution of individual eigen-components or their pairwise combinations into the asymptotic variation of the system energy. We propose the energy criterion for estimation of the system stability margins that uses an evaluation of energy accumulated in a group of weakly stable system modes. This approach is illustrated by calculating the energy of a band-pass filter.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0005117916120043</doi><tpages>18</tpages></addata></record> |
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| ispartof | Automation and remote control, 2016-12, Vol.77 (12), p.2132-2149 |
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| subjects | Bandpass filters CAE) and Design Calculus of Variations and Optimal Control Optimization Computer-Aided Engineering (CAD Control Decomposition Dynamic stability Dynamical systems Dynamics Eigenvalues Linear Systems Mathematical analysis Mathematics Mathematics and Statistics Mechanical Engineering Mechatronics Quadratic forms Robotics Stability analysis Systems analysis Systems stability Systems Theory Transfer functions |
| title | Energy approach to stability analysis of the linear stationary dynamic systems |
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