Mixing
what would be its solution in discrete as well as continous time
$begingroup$
If I have an equation like ( assume everything as its suitable dimension and all are real matrices, $p,q$ are real constants)
$(1)$ $x(k+1)= pf(x(k))+q(Aotimes B)x(k)$
$(2) dot x(t)=pf(x(t))+q(Aotimes B)x(t)$
for $(2)$, after taking Laplace transformation, it is equivalent to solve the system $(lambda I-qAotimes B)x(t)=pf(x(t))$ but after that, I am not aware how to proceed.
Thanks for helping.
In particular, if someone helps me with $B=I$, It would be helpfull too.
ordinary-differential-equations tensor-products matrix-equations discrete-time
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
$endgroup$
add a comment |
$begingroup$
If I have an equation like ( assume everything as its suitable dimension and all are real matrices, $p,q$ are real constants)
$(1)$ $x(k+1)= pf(x(k))+q(Aotimes B)x(k)$
$(2) dot x(t)=pf(x(t))+q(Aotimes B)x(t)$
for $(2)$, after taking Laplace transformation, it is equivalent to solve the system $(lambda I-qAotimes B)x(t)=pf(x(t))$ but after that, I am not aware how to proceed.
Thanks for helping.
In particular, if someone helps me with $B=I$, It would be helpfull too.
ordinary-differential-equations tensor-products matrix-equations discrete-time
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
$endgroup$
add a comment |
$begingroup$
If I have an equation like ( assume everything as its suitable dimension and all are real matrices, $p,q$ are real constants)
$(1)$ $x(k+1)= pf(x(k))+q(Aotimes B)x(k)$
$(2) dot x(t)=pf(x(t))+q(Aotimes B)x(t)$
for $(2)$, after taking Laplace transformation, it is equivalent to solve the system $(lambda I-qAotimes B)x(t)=pf(x(t))$ but after that, I am not aware how to proceed.
Thanks for helping.
In particular, if someone helps me with $B=I$, It would be helpfull too.
ordinary-differential-equations tensor-products matrix-equations discrete-time
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
$endgroup$
If I have an equation like ( assume everything as its suitable dimension and all are real matrices, $p,q$ are real constants)
$(1)$ $x(k+1)= pf(x(k))+q(Aotimes B)x(k)$
$(2) dot x(t)=pf(x(t))+q(Aotimes B)x(t)$
for $(2)$, after taking Laplace transformation, it is equivalent to solve the system $(lambda I-qAotimes B)x(t)=pf(x(t))$ but after that, I am not aware how to proceed.
Thanks for helping.
In particular, if someone helps me with $B=I$, It would be helpfull too.
ordinary-differential-equations tensor-products matrix-equations discrete-time
ordinary-differential-equations tensor-products matrix-equations discrete-time
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
edited Feb 25 at 7:24
Alexander Gruber♦
20.1k25103174
20.1k25103174
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
asked Jan 31 at 12:04
miosakimiosaki
2,43411537
2,43411537
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3094811%2fwhat-would-be-its-solution-in-discrete-as-well-as-continous-time%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3094811%2fwhat-would-be-its-solution-in-discrete-as-well-as-continous-time%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
