Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems
Statistical sensitivity in discrete-time state-space linear systems is defined, using a virtual system whose coefficients are stochastically varied. The necessary and sufficient condition for the mean-square asymptotical stability is obtained by analyzing the convergence of the state covariance matr...
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| Veröffentlicht in: | IEEE transactions on circuits and systems 1990-01, Vol.37 (1), p.72-80 |
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| container_title | IEEE transactions on circuits and systems |
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| creator | Iwatsuki, M. Kawamata, M. Higuchi, T. |
| description | Statistical sensitivity in discrete-time state-space linear systems is defined, using a virtual system whose coefficients are stochastically varied. The necessary and sufficient condition for the mean-square asymptotical stability is obtained by analyzing the convergence of the state covariance matrix of the virtual system. This condition determines an upper bound on the variance of coefficient variations that guarantees stochastic stability. Minimum-sensitivity structures can be synthesized by using two assumptions to simplify the sensitivity measure. The minimum-sensitivity structures have many more coefficients than the other canonical structures in general. The authors synthesize minimum-sensitivity structures that have fewer coefficients and lower sensitivity than the usual minimum-sensitivity structures. The number of coefficients depends on the pole-zero configuration of the transfer function. Two numerical examples show that the minimum-sensitivity structures have much lower sensitivity than the other realizations.< > |
| doi_str_mv | 10.1109/31.45693 |
| format | Article |
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The necessary and sufficient condition for the mean-square asymptotical stability is obtained by analyzing the convergence of the state covariance matrix of the virtual system. This condition determines an upper bound on the variance of coefficient variations that guarantees stochastic stability. Minimum-sensitivity structures can be synthesized by using two assumptions to simplify the sensitivity measure. The minimum-sensitivity structures have many more coefficients than the other canonical structures in general. The authors synthesize minimum-sensitivity structures that have fewer coefficients and lower sensitivity than the usual minimum-sensitivity structures. The number of coefficients depends on the pole-zero configuration of the transfer function. 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The necessary and sufficient condition for the mean-square asymptotical stability is obtained by analyzing the convergence of the state covariance matrix of the virtual system. This condition determines an upper bound on the variance of coefficient variations that guarantees stochastic stability. Minimum-sensitivity structures can be synthesized by using two assumptions to simplify the sensitivity measure. The minimum-sensitivity structures have many more coefficients than the other canonical structures in general. The authors synthesize minimum-sensitivity structures that have fewer coefficients and lower sensitivity than the usual minimum-sensitivity structures. The number of coefficients depends on the pole-zero configuration of the transfer function. Two numerical examples show that the minimum-sensitivity structures have much lower sensitivity than the other realizations.< ></description><subject>Asymptotic stability</subject><subject>Covariance matrix</subject><subject>Digital filters</subject><subject>Linear systems</subject><subject>Quantization</subject><subject>Stability analysis</subject><subject>Stochastic processes</subject><subject>Sufficient conditions</subject><subject>Transfer functions</subject><subject>Upper bound</subject><issn>0098-4094</issn><issn>1558-1276</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1990</creationdate><recordtype>article</recordtype><recordid>eNpVkM1LxDAUxIMoWFfBq7ccvXTNR9M2R1l0FRY8qOeSpC_4pO1KXtZl_3tXVwRPAzM_hmEYu5RiLqWwN1rOK1NbfcQKaUxbStXUx6wQwrZlJWx1ys6I3oUQrW3bgqXn7DJSxuAGTjARZvzEvONu6vmIE46b8Z9POW1C3iQgvsX8xiNsIfGwhhgxIEyZOE68RwoJMvCMI_ABJ3CJ044yjHTOTqIbCC5-dcZe7-9eFg_l6mn5uLhdlUFVOpdKCRmUE6CDj0qCC66RRkLt68ZrZZ3x2rumt6buTS3A7xdYV3mv91FQUc_Y9aE3pDVRgth9JBxd2nVSdN9fdVp2P1_t0asDigDwhx2yL8CuaJw</recordid><startdate>199001</startdate><enddate>199001</enddate><creator>Iwatsuki, M.</creator><creator>Kawamata, M.</creator><creator>Higuchi, T.</creator><general>IEEE</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>199001</creationdate><title>Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems</title><author>Iwatsuki, M. ; Kawamata, M. ; Higuchi, T.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c243t-2201c2a0e3cbf21eaca7151e6b67b329a5b3ba7d956d560ebeff9a4bb39a5c2f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1990</creationdate><topic>Asymptotic stability</topic><topic>Covariance matrix</topic><topic>Digital filters</topic><topic>Linear systems</topic><topic>Quantization</topic><topic>Stability analysis</topic><topic>Stochastic processes</topic><topic>Sufficient conditions</topic><topic>Transfer functions</topic><topic>Upper bound</topic><toplevel>online_resources</toplevel><creatorcontrib>Iwatsuki, M.</creatorcontrib><creatorcontrib>Kawamata, M.</creatorcontrib><creatorcontrib>Higuchi, T.</creatorcontrib><collection>CrossRef</collection><jtitle>IEEE transactions on circuits and systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Iwatsuki, M.</au><au>Kawamata, M.</au><au>Higuchi, T.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems</atitle><jtitle>IEEE transactions on circuits and systems</jtitle><stitle>T-CAS</stitle><date>1990-01</date><risdate>1990</risdate><volume>37</volume><issue>1</issue><spage>72</spage><epage>80</epage><pages>72-80</pages><issn>0098-4094</issn><eissn>1558-1276</eissn><coden>ICSYBT</coden><abstract>Statistical sensitivity in discrete-time state-space linear systems is defined, using a virtual system whose coefficients are stochastically varied. The necessary and sufficient condition for the mean-square asymptotical stability is obtained by analyzing the convergence of the state covariance matrix of the virtual system. This condition determines an upper bound on the variance of coefficient variations that guarantees stochastic stability. Minimum-sensitivity structures can be synthesized by using two assumptions to simplify the sensitivity measure. The minimum-sensitivity structures have many more coefficients than the other canonical structures in general. The authors synthesize minimum-sensitivity structures that have fewer coefficients and lower sensitivity than the usual minimum-sensitivity structures. The number of coefficients depends on the pole-zero configuration of the transfer function. Two numerical examples show that the minimum-sensitivity structures have much lower sensitivity than the other realizations.< ></abstract><pub>IEEE</pub><doi>10.1109/31.45693</doi><tpages>9</tpages></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Asymptotic stability Covariance matrix Digital filters Linear systems Quantization Stability analysis Stochastic processes Sufficient conditions Transfer functions Upper bound |
| title | Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems |
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