This is quite interesting -- you seem to have stumbled upon a conflict between the memoir class and biblatex. Using the book class correctly yields "ibid." for citations no. 3 and 6 in your first example, but using the memoir class doesn't.
% Using the "book" class correctly yields "ibid." for citations no. 3 and 6
\documentclass{book}
% But using the "memoir" class doesn't
% \documentclass{memoir}
\usepackage[style=verbose-ibid]{biblatex}
\begin{filecontents}{\jobname.bib}
@misc{Book1,
author = {Author, A.},
year = {2001},
title = {Alpha},
}
@misc{Book2,
author = {Buthor, B.},
year = {2002},
title = {Bravo},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
Check.\footcite{Book1}
Check.\footcite{Book1}
Check.\footnote{\cite{Book1}.}
Check.\footcite{Book1}
Check.\footcite{Book2}
Check.\footnote{\cite{Book2}.}
\end{document}
Second solution
Edited again, so most multicite commands work.
Edited so \footcite now works.
A reasonably effective solution that preserves many of biblatex's featuers is provided by adjusting the way the year gets printed in citations. This can be done by redifining the commands associated to cite:year and cite:extrayear. This has the advantage of preserving the ibidem feature.
The code below includes a sample bibliography and then the main file with the redefined citation code.
\begin{filecontents}{test.bib}
@Article{Test,
author = {Author, A. N.},
title = {Article title},
year = 2005,
pages = {10-20},
journal = {Jour.},
vol = {100}
}
@Article{Test2,
author = {Author, A. N.},
title = {Second article},
year = 2005,
pages = {10-20},
journal = {Jour.},
vol = {100}
}
@Article{Test3,
author = {Author, A. B.},
title = {Third article},
year = 2005,
pages = {10-20},
journal = {Jour.},
vol = {100}
}
@Article{Test4,
author = {Author, A. N.},
title = {Fourth article},
year = 2007,
pages = {10-20},
journal = {Jour.},
vol = {100}
}
\end{filecontents}
\documentclass{article}
\usepackage[style=authoryear-icomp,autocite=plain]{biblatex}
\addbibresource{test.bib}
\renewbibmacro*{cite:labelyear+extrayear}{%
\iffieldundef{labelyear}
{}
{\iftoggle{blx@footnote}
{\printtext[bibhyperref]{%
\printfield{labelyear}%
\printfield{extrayear}}}
{\footnote{\printtext[bibhyperref]{%
\printfield{labelyear}%
\printfield{extrayear}}}}}}
\renewbibmacro*{cite:extrayear}{%
\iffieldundef{extrayear}
{}
{\iftoggle{blx@footnote}
{\printtext[bibhyperref]{\printfield{extrayear}}}%
{\footnote{\printtext[bibhyperref]{%
\printfield{labelyear}%
\printfield{extrayear}}}}}}
\renewcommand{\compcitedelim}{\space}
\begin{document}
\thispagestyle{empty}
\autocite{Test} and
\autocite[page 3]{Test}.
Some text \parencite{Test2}.
Here is a footnote citation\footcite{Test}.
\autocite{Test,Test4,Test3}.
\printbibliography
\end{document}
As the above shows this works with \autocite, \parencite and accepts their optional arguments. In this style \autocite is the same as \cite.
I haven't demonstrated \textcite, though its ouptut may be useful sometimes; \footcite has also been set up to work, thanks to biblatex's blx@footnote toggle that detects whether we are in a footnote or not.
The code also takes care of most multiple citations \cite{ref1,ref2}. However, there is a spurious comma, if ref1 and ref2 are two publications from the same author in the same year. Fixing that requires, more substanitial rewriting of the citation style file: each of the commands \cite, \textcite, etc. in author-icomp.cbx contains an explicit comma via \setunit{\addcomma}, that needs to be deleted.
Original solution
Here is a repost of the original solution, as this apparently helps the OP best. It simply defines a newcommand \citepfy (plain-foot-year) that calls \citeauthor followed by a modified \footcite command that produces only the year. It does not accept any of the optional arguments cite commands in biblatex usually do.
\begin{filecontents}{b.bib}
@Article{Test,
author = {Author, A. N.},
title = {Article title},
year = 2005,
pages = {10-20},
journal = {Jour.},
vol = {100}
}
\end{filecontents}
\documentclass{article}
\usepackage[style=authoryear-icomp]{biblatex}
\addbibresource{b.bib}
\newcommand{\citepfy}[1]{\citeauthor{#1}\footyearcite{#1}}
\DeclareCiteCommand{\footyearcite}[\mkbibfootnote]
{\usebibmacro{cite:init}%
\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\usebibmacro{citeyear}}
{}
{\usebibmacro{cite:postnote}}
\begin{document}
\citepfy{Test}
\printbibliography
\end{document}
Best Answer
You can switch on and off the cite tracker feature with
\citetrackertrueand\citetrackerfalsecommands. A second option is to use\mancite(to be used in the same context where the manual citation appears);\mancitealso execute the hook defined with\OnManualCitation. The third option is to use\citereset(it reset all subsequent citations), and there is a global option with the same name taking a document subdivision (e.g.,part,chapter,...) as its argument.biblatexalso provides apagetrackeroption whose possible values aretrue,false,pageandspreadfor the case of a repeated citation in a new page.