Document:

<PAGE>   1
                                                                    EXHIBIT 4.26

                                                               November 12, 1999

Illinois Superconductor Corporation
451 Kingston Court
Mount Prospect, Illinois 60056

Ladies and Gentlemen:

         This letter amends the letter agreement ("Agreement") captioned
"Additional Investment" by and among Elliott Associates, L.P., Westgate
International, L.P., and Alexander Finance, L.P. ("Investors") and Illinois
Superconductor Corporation ("Company"), dated November 5, 1999, by deleting the
last two sentences of Section 12 of the Agreement and replacing those sentences
with the following:

         Notwithstanding anything to the contrary contained herein or in the
         Notes and Warrants, unless and until the foregoing Charter Amendment is
         effected, and except with respect to determining the redemption rights
         referred to above, the Notes and Warrants held by the undersigned on
         the date of the Agreement after giving effect thereto and regardless of
         whether such Notes and Warrants are transferred at any time (such Notes
         and Warrants are the "Investor Notes and Warrants") shall represent a
         right in the aggregate, allocated pro rata among them, to acquire
         (including with respect to in-kind interest payments paid and to be
         paid) that number of shares (but not more than that number of shares)
         of Common Stock equal to the number of shares of Common Stock currently
         authorized by the Company's Certificate of Incorporation reduced by the
         sum of (i) the number of shares and shares subject to options
         outstanding on the date hereof, (ii) the number of shares subject to
         additional options granted under the Illinois Superconductor
         Corporation 1993 Stock Option Plan, as amended through June, 1999
         ("Plan"), (iii) the

<PAGE>   2

         number of shares subject to any options granted outside the Plan with
         the written consent of the undersigned, and (iv) the number of shares
         (including with respect to in-kind interest payments paid and to be
         paid through November 5, 2000) that the Notes and Warrants other than
         the Investor Notes and Warrants carry the right to acquire.

         This letter amending the Agreement may be executed in multiple
counterparts which together shall constitute the amendment to the Agreement. As
modified herein, the documents relating to the Notes and Warrants remain in full
force and effect.

                                      Sincerely,

                                      ELLIOTT ASSOCIATES, L.P.

                                      By: /s/ PAUL SINGER
                                      -------------------

                                      WESTGATE INTERNATIONAL, L.P.
                                          By:  Martley International, Inc.
                                                Attorney-in-Fact

                                                By: /s/ PAUL SINGER
                                                    -----------------------

                                      ALEXANDER FINANCE, L.P.

                                          By: /s/ BRADFORD T. WHITMORE
                                              -----------------------------

AGREED TO AND ACCEPTED:

ILLINOIS SUPERCONDUCTOR CORPORATION

By: /s/ CYNTHIA QUIGLEY
    ----------------------------------

                                      -2-<PAGE>   1
                                                                    EXHIBIT 4.27

                            Elliott Associates, L.P.
                                712 Fifth Avenue
                            New York, New York 10019

                          Westgate International, L.P.
                      c/o Stonington Management Corporation
                                712 Fifth Avenue
                            New York, New York 10019

                             Alexander Finance, L.P.
                               1560 Sherman Avenue
                            Evanston, Illinois 60201

                                December 28, 1999

Illinois Superconductor Corporation
451 Kingston Court
Mt. Prospect, Illinois 60056

         RE: EXERCISE OF OPTION

Ladies and Gentlemen:

         Reference is made to the Investment Agreement, dated as of November 5,
1999 (as amended by the letter dated November 12, 1999) (the "Investment
Agreement"), by and among you (the "Company") and the undersigned (the
"Investors"). Capitalized terms used herein without definition have the meaning
set forth in the Investment Agreement.

         1.  Exercise of Option.
             -------------------

         (a) Pursuant to Section 7 of the Investment Agreement, the Investors
hereby notify the Company of their exercise of the option, contained in such
section, to purchase additional Notes and Warrants which shall contain the terms
and provisions described in such section.

         (b) Pursuant to the foregoing exercise, the Investors shall purchase
(the "Option Purchase") an aggregate of $1,000,000 principal amount of Notes and
Warrants to purchase 400,000 shares of Common Stock, in the respective amounts
set forth on Schedule I hereto, for aggregate consideration of $1,000,000 (the
"Option Purchase Price"). This option exercise shall be without prejudice to the
rights of the Investors, pursuant to Section 7 of the Investment Agreement, to
invest up to an additional $4,000,000 in the Company.

<PAGE>   2

         2.  Closing of Option Purchase.
             ---------------------------

         (a) The closing of the Option Purchase shall take place at the offices
of Kleinberg, Kaplan, Wolff & Cohen, P.C. on December 29, 1999 (the "Closing
Date") at 1 p.m. Eastern Standard Time.

         (b) The Notes and Warrants purchased pursuant to the Option Purchase
shall be deemed to be outstanding on the Closing Date for all purposes. Within
one day of the Closing Date, the Company shall deliver to the Investors, in
physical form, the Notes and Warrants purchased by them pursuant to the Option
Purchase. The delivery of payment by wire transfer to an account designated by
the Company by each Investor of the portion of the Option Purchase Price
applicable to it as set forth in Schedule I shall constitute a payment delivered
to the Company in satisfaction of such Investor's obligation to pay its share of
the Option Purchase Price hereunder.

         (c) In addition to the foregoing, within fourteen days of the Closing
Date, the Company shall deliver in physical form, the Notes and Warrants
purchased by the undersigned from the Company on November 5, 1999.

         (d) The Company agrees to pay the legal fees and disbursements incurred
by the Investors in connection with the Option Purchase and shall pay the
invoice for such fees and disbursements within seven days of the receipt
thereof.

         3. Representations and Warranties.
            -------------------------------

         (a) The Company hereby restates, as of the date hereof, the
representations and warranties set forth in Section 8 of the Investment
Agreement, with respect to the Notes and Warrants being issued pursuant to the
Option Purchase, except as set forth on Schedule II, hereto. For purposes of the
foregoing restatement of representations, (i) references to Transaction
Documents shall refer only to this Agreement and, with respect to solely the
consummation of the Option Purchase, the Transaction Documents referred to in
the Investment Agreement, and (ii) the date referred to in Section 2.1(s) shall
be deemed to refer to November 15, 1999.

         (b) The Investors hereby restate the representations set forth in
Section 9(a) of the Investment Agreement with respect to the Notes and Warrants
being purchased pursuant to the Option Purchase.

                            [signature page follows]

                                       2
<PAGE>   3
         Please indicate your acceptance and agreement of the terms contained
herein by countersigning this Agreement and returning a signed copy to the
undersigned.

                                           Sincerely,

                                           ELLIOTT ASSOCIATES, L.P.

                                           By: /s/ ELLIOT GREENBERG
                                               ---------------------------------
                                           Elliot Greenberg, Vice-President

                                           WESTGATE INTERNATIONAL, L.P.
                                               By:  Martley International, Inc.
                                                     Attorney-in-Fact

                                               By: /s/ ELLIOT GREENBERG
                                                   -----------------------------
                                               Elliot Greenberg, Vice-President

                                           ALEXANDER FINANCE, L.P.

                                           By: /s/ Bradford T. Whitmore
                                               ---------------------------------
                                               Bradford T. Whitmore
                                               President:  Bun Partners, Inc.
                                                           its General Partner

AGREED TO AND ACCEPTED

ILLINOIS SUPERCONDUCTOR CORPORATION

By: /s/ CYNTHIA QUIGLEY
    ---------------------------------------

                                       3
<PAGE>   4

                                   SCHEDULE I

<TABLE>
<CAPTION>
                                                     PRINCIPAL AMOUNT              AMOUNT OF
PURCHASER                         PURCHASE PRICE     OF NOTES PURCHASED      WARRANTS PURCHASED
---------                         --------------     ------------------      ------------------
<S>                                  <C>                  <C>                       <C>
Elliott Associates, L.P.             $277,778             $277,778                  111,111
Westgate International, L.P.         $277,778             $277,778                  111,111
Alexander Finance, LP                $444,444             $444,444                  177,778
</TABLE>

<PAGE>   5
                Schedule II to Agreement Dated December 28, 1999
                ------------------------------------------------

         The Company generally incorporates information from its SEC filings as
disclosures for these schedules. The Company further notes that:

2.1(c): The 3rd Quarter 1999 10-Q has the Company's current capitalization prior
to giving effect to these transactions. Additional holders of 5% of the
Company's Common Stock, if any, may be disclosed in Schedules 13D or 13G filed
with the Securities and Exchange Commission. Options have continued to be
granted.

2.1(d): As recognized in Section 12 of the Investment Agreement, additional
shares must be authorized and a charter amendment is necessary to authorize such
shares.

2.1(e)/(f): See 2.1(d) above with respect to the need for a charter amendment.
The factoring agreement with Franklin Capital will be in breach if a lien is
created on the inventory and accounts without the prior written consent of the
factor. The Company will not list shares of its Common Stock, and will register
such shares as and when required by the Registration Rights Agreement as
modified by Section 5 of the Investment Agreement. The Company will reflect the
Option Purchase in a Form 8-K filing and a Form S-2 supplemental filing.

2.1(g): To the Company's knowledge, there is no pending litigation except (i)as
disclosed in the SEC filings, and (ii) Steve Levy v. Illinois Superconductor
Corporation, filed in Delaware Chancery Court on or about December 14, 1999.

2.1(h):See 2.1(e)/(f), above.

2.1(i): The Company has not recently reviewed the voluminous schedules
previously delivered and the Company does not now make or update such
representations and schedules.

2.1(k): The Disclosure Materials also include the Company's Annual Report on
Form 10-K for the year ended December 31, 1998, its Quarterly Reports on Form
10-Q for the quarters ended March 31, June 30, 1999 and September 30, 1999, and
its Current Reports on Form 8-K filed in 1999. Elliott and Grace have been
updated on the Company's financial and business situation, including at a
meeting with those investors during their due diligence in connection with their
November, 1999 investment in the Company, and as a result of affiliates of
Elliott having joined the Company's board of directors in November, 1999. That
information, including the written handouts from the aforementioned due
diligence meeting, is incorporated by reference.

2.1(l) The obligations to Franklin Capital under the factoring agreement are
pari passu with the notes held by Elliott and Grace, including the 6% Notes, but
may in certain respects have a senior lien.

2.1(p): Registration under Form S-3 may no longer be available to the Company. A
registration under Form S-2 may be available.

2.1(s): See SEC filings. Elliott and Grace are aware of the terms of the
factoring agreement with Franklin Factor.

                                       5

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