<PAGE>   1
                                                                   EXHIBIT 10.34

                           PEROT SYSTEMS CORPORATION
                             1991 STOCK OPTION PLAN

                             STOCK OPTION AGREEMENT


                        NON-QUALIFIED STOCK OPTION GRANT

   THIS STOCK OPTION AGREEMENT IS NOT VALID UNTIL A PROPERLY EXECUTED ORIGINAL
   COPY IS RETURNED TO PEROT SYSTEMS. IF YOU DO NOT RETURN A PROPERLY EXECUTED
   ORIGINAL COPY WITHIN 60 DAYS AFTER THE EFFECTIVE DATE SET FORTH BELOW, YOU
 WILL BE DEEMED TO HAVE REJECTED THE AGREEMENT UNLESS PEROT SYSTEMS, IN ITS SOLE
                       DISCRETION, DETERMINES OTHERWISE.

Participant:              <<First Name>> <<Last Name>>
Effective Date:           July 20, 1998
Option Shares:            <<Option Shares>>
Exercise Price:           The Exercise Price will be the price at which shares
                          of Common Stock are offered to the public in an
                          initial public offering, provided that if the Company
                          does not complete an initial public offering of
                          Common Stock within six months after the Effective
                          Date, the Exercise Price will be a price established
                          by the Board not later than January 20, 1999.
Vesting Schedule:         100% of the Option Shares on the third anniversary of
                          the Effective Date
Expiration Date:          Five years after the Effective Date, unless
                          terminated earlier under the Agreement or the Plan.

BY SIGNING THIS AGREEMENT, THE PARTICIPANT:

o        Agrees to be bound by the terms of this Agreement and the Plan;
o        Acknowledges receiving an electronic or paper copy of (1) the Plan, (2)
         the Prospectus for the Plan, and (3) Perot Systems' most recent Annual
         Report on Form 10-K; and
o        Consents to receiving delivery of the all future communications and
         required documents relating to the Plan or this Agreement via TRAIN or
         other electronic transmission.


<<First Name>> <<Last Name>>            PEROT SYSTEMS CORPORATION


Signature:                              By:                                   
           -----------------               -----------------------------------
Date:                                            Chairman of the Board
     -----------------------



              [The remainder of this page is intentionally blank.]





1991 Stock Option Plan           Page 1 of 10            Stock Option Agreement

<PAGE>   2
1.       Certain Definitions. As used in this Agreement, the following terms
         have the meanings indicated:

         (a)      "Agreement" means this Stock Option Agreement between Perot
                  Systems and Participant.

         (b)      "Committee" means the Board of Directors of Perot Systems or
                  the committee of the Board, Chief Executive Officer or other
                  officer of Perot Systems appointed to administer the Plan.

         (c)      "Common Stock" means the Class A Common Stock, $.01 par value
                  per share, of Perot Systems.

         (d)      "Company" means Perot Systems and its majority-owned
                  subsidiaries.

         (e)      "Confidential Information" means all written, machine
                  reproducible, oral and visual data, information and material,
                  including but not limited to the terms of this Agreement and
                  the Plan, business, financial and technical information,
                  computer programs, documents and records (including those that
                  Participant develops in the scope of his or her employment)
                  that (i) the Company or any of its customers or suppliers
                  treats as proprietary or confidential through markings or
                  otherwise, (ii) relates to the Company or any of its customers
                  or suppliers or any of their business activities, products or
                  services (including software programs and techniques) and is
                  competitively sensitive or not generally known in the relevant
                  trade or industry, or (iii) derives independent economic value
                  from not being generally known to, and is not readily
                  ascertainable by proper means by, other persons who can obtain
                  economic value from its disclosure or use. Confidential
                  Information does not include any information or material that
                  is approved by Perot Systems for unrestricted public
                  disclosure.

         (f)      "Effective Date" means the date set forth on the first page of
                  this Agreement on which the term of this Agreement commenced.

         (g)      "Expiration Date" means the date and time as of which the
                  Option expires, which is the earlier of (i) the close of
                  business on the date one year (two years if the Vesting Period
                  is three years or less) after the entire Option has Vested or
                  (ii) the date and time as of which all rights to exercise the
                  Option are terminated under Section 2(d).

         (h)      "Market Value" of a share of Purchased Stock on a given date
                  means (i) if the Purchased Stock is Publicly Traded, the
                  closing sale price for Purchased Stock, as determined in good
                  faith by the Board of Directors, on such date or, if no
                  closing sale price is available for such date, on the most
                  recent prior date for which a closing sale price is available
                  or, if no closing sale price is available, the closing bid
                  price, as so determined, on such date or, if no closing bid
                  price is available for such date, the closing bid price on the
                  most recent prior date for which a closing bid price is
                  available, or (ii) if the Purchased Stock is not Publicly
                  Traded, its fair market value, as determined in good faith by
                  the Board of Directors, as of the most recent Valuation Date
                  on or before such date.





1991 Stock Option Plan           Page 2 of 10            Stock Option Agreement

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         (i)      "Net Investment Proceeds," with respect to any share of
                  Purchased Stock sold or otherwise transferred by Participant
                  or Participant's successor in interest, means the greater of
                  the value of the gross proceeds received for such share or the
                  Market Value of such share on the date of sale or transfer
                  less, in either case, (i) the exercise price of the Option for
                  such share plus simple interest on such amount at the rate of
                  8% per annum to the date of the sale or transfer, (ii) any
                  reasonable and customary commission paid for the sale or
                  transfer, and (iii) the verified amount of any income taxes
                  paid or payable on the sale or transfer.

         (j)      "Option" means the right and option evidenced by this
                  Agreement.

         (k)      "Participant" means the individual named on the first page of
                  this Agreement.

         (l)      "Perot Systems" means Perot Systems Corporation, a Delaware
                  corporation.

         (m)      "Plan" means Perot Systems' 1991 Stock Option Plan, as amended
                  and restated as of July 17, 1998, as amended from time to
                  time.

         (n)      "Publicly Traded" means Purchased Stock has been listed on a
                  registered national securities exchange or approved for
                  quotation in the National Association of Securities Dealers
                  Automated Quotation ("NASDAQ") system.

         (o)      "Purchased Stock" means any Common Stock purchased upon the
                  exercise of this Option, together with any successor security,
                  property or cash issued or distributed by Perot Systems or any
                  successor entity, whether by way of merger, consolidation,
                  share exchange, reorganization, liquidation, recapitalization
                  or otherwise.

         (p)      "Termination for Substantial Misconduct" means termination of
                  employment for conduct resulting in a felony conviction of the
                  Participant; actions involving moral turpitude, theft, or
                  dishonesty in a material matter; breach of any obligation
                  under Section 5 of this Agreement; or failure by Participant
                  to carry out the directions, instructions, policies, rules,
                  regulations, or decisions of the Board of Directors of Perot
                  Systems including, without limitation, those relating to
                  business ethics and the ethical conduct of the business of the
                  Company.

         (q)      "Transfer" or "transfer" or derivations thereof includes any
                  sale, assignment, gift, pledge, encumbrance, hypothecation,
                  mortgage, exchange or any other disposition.

         (r)      "Valuation Date" means each date as of which the Board of
                  Directors determines the Market Value of Purchased Stock.

         (s)      "Vesting," or "vesting" or derivations thereof with respect to
                  any Option issued under this Agreement, means receiving the
                  right to exercise the Option.





1991 Stock Option Plan           Page 3 of 10            Stock Option Agreement

<PAGE>   4
         (t)      "Vesting Period" means the period of time commencing on the
                  Effective Date of this Agreement and ending on the date on
                  which the entire Option has Vested.

2.       Grant of Option; Exercise of Option; Purchase of Stock.

         (a)      Subject to the terms, conditions, and restrictions set forth
                  in the Plan (which is incorporated herein by reference) and
                  this Agreement, Perot Systems hereby grants to Participant,
                  and Participant hereby accepts from Perot Systems, the option
                  to purchase from Perot Systems

                  (i)    the number of shares of Common Stock specified as
                  the "Option Shares" on the first page of this Agreement,

                  (ii)   at the purchase price per share of Common Stock 
                  specified as the "Exercise Price" on the first page of this
                  Agreement,

                  (iii)  which option will Vest in Participant in accordance 
                  with the Vesting Schedule specified on the first page of this
                  Agreement.

                  The Option shall only continue to Vest only for as long as
                  Participant is an employee of Company, unless the Committee,
                  in its sole discretion, agrees in writing otherwise.
                  Participant will have the right to exercise the Vested Option
                  and purchase Common Stock after the Option Vests as provided
                  in Section 2(d) below.

         (b)      The purchase price of shares as to which the Option is
                  exercised must be paid to Perot Systems at the time of the
                  exercise either in cash or in such other consideration as the
                  Committee may approve having a total fair market value, as
                  determined by the Committee, equal to the purchase price, or a
                  combination of cash and such other consideration.

         (c)      The Committee may elect to assist Participant in satisfying an
                  obligation to pay or withhold taxes required as a result of
                  the exercise of this Option by accepting shares of Purchased
                  Stock at Market Value to satisfy the tax obligation. The
                  shares of Purchased Stock accepted may be either shares
                  withheld upon the exercise of this Option or other shares
                  already owned by Participant. In determining whether to
                  approve acceptance of Purchased Stock to satisfy such a tax
                  obligation, the Committee may consider whether the shares
                  proposed to be delivered are subject to any holding period or
                  other restrictions on transfer and may waive or arrange for
                  the waiver of any such restrictions.

         (d)      The Option is only exercisable as to Vested Options. Once
                  Vested, the Option may be exercised until the Expiration Date,
                  provided, however, (i) if the Participant ceases to be an
                  employee for any reason other than death, the Option may be
                  exercised only for sixty days after the date of cessation of
                  employment, and in any case no later than the Expiration Date,
                  and (ii) if the Participant ceases to be an Employee because
                  of death of the Participant, the Option may be exercised by
                  the Participant's estate only for two years after the
                  Participant's Death and in any case no later than the
                  Expiration Date.





1991 Stock Option Plan           Page 4 of 10            Stock Option Agreement

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         (e)      The Option is exercisable by delivery of an exercise notice,
                  in the form and format and by the method approved by Perot
                  Systems stock administrator, which form and format may be
                  electronic and solely available by access through Perot
                  Systems internal computer network, which notice will state the
                  election to exercise the Option, the number of Vested shares
                  of Common Stock with respect to which the Option is being
                  exercised, and such other representations and agreements as
                  may be required by the Company in accordance with the terms of
                  the Plan. The Option will be deemed to be exercised upon
                  receipt by the Company of such exercise notice and the
                  purchase price of the Vested shares of Common Stock as to
                  which the Option is exercised, provided that Participant has
                  concurrently made adequate provision for fulfilling all
                  applicable tax withholding requirements and other tax
                  obligations.

3.       Restrictions on Transfer. The following restrictions on transfer apply
         unless the Committee otherwise agrees in writing or unless the transfer
         is by will or the laws of descent and distribution upon Participant's
         death:

         (a)      The Option may not be sold or otherwise transferred and is
                  exercisable only by Participant during Participant's lifetime.

         (b)      Shares of Purchased Stock may not be sold or otherwise
                  transferred unless the holder has given Perot Systems any
                  notice required under Section 4(a) and Perot Systems has
                  waived in writing any right it has to buy back the shares
                  under Section 4(a).

         (c)      Shares of Purchased Stock may not be sold or otherwise
                  transferred for six months after the Purchased Stock (or stock
                  of the same class as the Purchased Stock) is Publicly Traded.

         Perot Systems is not obligated to recognize any purported sale or other
         transfer of the Option or any Purchased Stock in violation of this
         Section 3 and, unless it elects to do otherwise, may treat any such
         purported sale or transfer as null, void, and of no effect.

4.       Rights to Buy Back Purchased Stock and to Require Payback of Certain
         Profits.

         (a)      At any time before the Purchased Stock is Publicly Traded, if
                  Participant or any subsequent holder of shares of Purchased
                  Stock desires or is obligated to sell or otherwise transfer
                  any such shares (including any distribution to heirs or other
                  beneficiaries of Participant's estate), the holder is required
                  to give Perot Systems written notice of the proposed sale or
                  transfer, including notice of the proposed purchaser or
                  transferee, and, for a period of 30 days after receipt of such
                  notice, Perot Systems will have the right to buy back such
                  shares for cash at a purchase price equal to the Market Value.

         (b)      If the Committee discovers that Participant has engaged in any
                  conduct prohibited by Section 5 or if Participant ceases to be
                  employed by the Company and the Committee, in its sole
                  discretion, determines that Participant's cessation of
                  employment resulted from a Termination for Substantial 
                  Misconduct or would have resulted in a Termination for 




1991 Stock Option Plan           Page 5 of 10            Stock Option Agreement

<PAGE>   6
                  Substantial Misconduct had the relevant facts been known at
                  the time of Participant's cessation of employment, Perot
                  Systems will have the right for 150 days after the Committee
                  discovers the relevant facts to cancel any unexercised Option,
                  whether or not Vested, and to buy back from Participant any
                  shares of Purchased Stock then owned by Participant, at a
                  purchase price equal to the price per share paid by
                  Participant for the shares plus simple interest on such amount
                  at the rate of 8% per annum from the date of payment by
                  Participant to the date of tender of payment by Perot Systems
                  as set forth in Section 4(c) below, and the right to require
                  Participant to pay back to Perot Systems in cash the Net
                  Investment Proceeds with respect to any shares of Purchased
                  Stock that have been sold or otherwise transferred by
                  Participant.

         (c)      Whenever Perot Systems has a right to buy back shares of
                  Purchased Stock or to require Participant to pay back to Perot
                  Systems Participant's Net Investment Proceeds with respect to
                  any shares of Purchased Stock under this Section 4, Perot
                  Systems may exercise its right by notifying Participant or the
                  subsequent holder of Perot Systems' election to exercise its
                  right within the designated exercise period. In the case of a
                  buyback under Section 4(a) or Section 4(b), the giving of such
                  notice will give rise to an obligation on the part of
                  Participant or the subsequent holder to tender to Perot
                  Systems, within 10 days, any previously issued certificate
                  representing shares of Purchased Stock to be bought back, duly
                  endorsed in blank or having a duly executed stock power
                  attached in proper form for transfer. If any such certificate
                  is not tendered within 10 days, Perot Systems may cancel any
                  outstanding certificate representing shares to be bought back.
                  Perot Systems is required to tender the purchase price for
                  shares to be bought back under this Section 4 within 20 days
                  of giving notice of its election to exercise its right to buy
                  back shares. If the person from whom the shares are to be
                  bought back has not complied with an obligation to return a
                  certificate representing shares to be bought back, however,
                  Perot Systems is not required to tender the purchase price
                  until 20 days after the certificate is returned or 20 days
                  after it cancels the certificate, whichever occurs first.

5.       Non-Competition and Non-Disclosure. Participant acknowledges that: (i)
         in the course and as a result of employment with the Company,
         Participant will obtain special training and knowledge and will come in
         contact with the Company's current and potential customers, which
         training, knowledge, and contacts would provide invaluable benefits to
         competitors of the Company; (ii) the Company is continuously developing
         or receiving Confidential Information, and that during Participant's
         employment he or she will receive Confidential Information from the
         Company, its customers and suppliers and special training related to
         the Company's business methodologies; and (iii) Participant's
         employment by Company creates a relationship of trust that extends to
         all Confidential Information that becomes known to Participant.
         Accordingly, and in consideration of Perot Systems' granting this
         Option to Participant, Participant agrees that Perot Systems will be
         entitled to terminate all rights to exercise the Option and to exercise
         the rights specified in Section 4 above if Participant does any of the
         following without the prior written consent of the Company:

         (a)      while employed by the Company or within one year thereafter:





1991 Stock Option Plan           Page 6 of 10            Stock Option Agreement

<PAGE>   7
                  (i)      competes with, or engages in any business that is
                           competitive with, the Company within 250 miles of any
                           location at which Participant was employed by or
                           provided services to the Company;

                  (ii)     solicits or performs services, as an employee,
                           independent contractor, or otherwise, for any person
                           (including any affiliates or subsidiaries of that
                           person) that is or was a customer or prospect of the
                           Company during the two years before Participant's
                           employment with the Company ended if Participant
                           solicited business from or performed services for
                           that customer or prospect while employed by Company;
                           or

                  (iii)    recruits, hires, or helps anyone to recruit or hire
                           anyone who was an employee of Perot Systems, or of
                           any of its customers for whom Participant performed
                           services of from whom Participant solicited business,
                           within the six months before Participant's employment
                           with the Company ended; or

         (b)      discloses or uses any Confidential Information, except in
                  connection with the good faith performance of Participant's
                  duties as an employee or, solely with respect to the terms of
                  this Agreement or the Plan, to Participant's spouse; or fails
                  to take reasonable precautions against the unauthorized
                  disclosure or use of Confidential Information; or fails, upon
                  Perot Systems' request, to execute and comply with a third
                  party's agreement to protect its confidential and proprietary
                  information; or solicits or induces the unauthorized
                  disclosure or use of Confidential Information.

         If any court of competent jurisdiction finds any provision of this
         Section 5 to be unreasonable, then that provision shall be considered
         to be amended to provide the broadest scope of protection to the
         Company that such court would find reasonable and enforceable.

6.       Compliance with Securities Laws. Participant hereby agrees that, upon
         demand by Perot Systems, any person exercising this Option, at the time
         of such exercise, will deliver to Perot Systems a written
         representation to the effect that the shares of Purchased Stock being
         acquired are being acquired for investment and not with a view to any
         resale or distribution thereof. Participant further agrees that neither
         Participant nor any successor in interest of Participant will sell or
         otherwise transfer the Option or any shares of Purchased Stock in any
         way that might result in a violation of any federal or state securities
         laws or regulations. Participant further acknowledges and agrees that
         Perot Systems may require Participant or any subsequent holder of the
         Option or of any shares of Purchased Stock to provide Perot Systems,
         prior to any sale or other transfer, with such other representations,
         commitments, and opinions regarding compliance with applicable
         securities laws and regulations as Perot Systems may deem necessary or
         advisable.

7.       Stock Certificates; Rights as Shareholder. Perot Systems or its
         designee may retain for safekeeping all certificates representing
         shares of Purchased Stock. Each such certificate will bear such legends
         as the Committee determines are necessary or appropriate. Whether or
         not certificates representing shares of Purchased Stock have been
         issued or delivered, Participant will have all the rights of a
         shareholder of Purchased Stock, including voting, dividend and





1991 Stock Option Plan           Page 7 of 10            Stock Option Agreement

<PAGE>   8
         distribution rights, with respect to shares of Purchased Stock owned by
         Participant. Participant will not have any rights as a shareholder with
         respect to any shares of Purchased Stock subject to the Option before
         the date of issuance to Participant of shares upon exercise of the
         Option.

8.       Income Tax Withholding. Participant shall, upon request by the Company,
         reimburse the Company for, or the Company may withhold from sums or
         property otherwise due or payable to Participant, any amounts the
         Company is required to remit to applicable taxing authorities as income
         tax withholding with respect to the Option or any Purchased Stock. If
         shares of Purchased Stock are withheld for such purpose, they will be
         withheld at Market Value. If Participant fails to reimburse the Company
         for any such amount when requested, the Company has the right to
         recover that amount by selling or canceling sufficient shares of any
         Purchased Stock held by Participant.

9.       Compliance with Plan. If the provisions of the Plan are inconsistent
         with the provisions of this Agreement, the provisions of the Plan
         supersede the provisions of this Agreement.

10.      Notices.

         (a)      All notices or other communications relating to this Plan or
                  any other matter relating to this Agreement given to the
                  Committee, Perot Systems, or any Company will be deemed
                  delivered on the day the notice or other communication is
                  received in tangible written form by the Stock Administrator
                  at Perot Systems' corporate headquarters address, provided
                  that such notice is in the form specified by Perot Systems.

         (b)      All notices or other communications relating to this Plan or
                  any other matter relating to this Agreement given to a
                  Participant by the Committee, Perot Systems, or any Company
                  will be deemed delivered on the first day the notice or other
                  communication is (1) personally delivered to that person, (2)
                  electronically transmitted to a person who on the date of that
                  transmission either is an employee of any Company or has
                  consented to receiving notices by electronic transmission to
                  the last known electronic transmission address of that person,
                  provided that an acknowledgement of receipt is returned, or
                  (3) placed in the official government mail of the country of
                  the sender in an envelope with proper postage paid addressed
                  to the last known address of that person as reflected in Perot
                  Systems' personnel or stock records.

         (c)      Either party may at any time change its address for
                  notification purposes by giving the other written notice of
                  the new address and the date upon which it will become
                  effective.

         (d)      CONSENT TO ELECTRONIC DELIVERY OF NOTICES, PLAN DOCUMENTS AND
                  PROSPECTUSES. BY EXECUTING THIS AGREEMENT, THE PARTICIPANT
                  WILL BE DEEMED TO CONSENT TO RECEIVING COPIES OF ALL NOTICES
                  AND OTHER COMMUNICATIONS RELATING TO THE PLAN AND THIS
                  AGREEMENT BY ELECTRONIC TRANSMISSION, INCLUDING BUT NOT
                  LIMITED TO THE PROSPECTUS RELATING TO THE PLAN, ALL
                  PARTICIPATION MATERIALS, AND ALL OTHER DOCUMENTS REQUIRED TO
                  BE DELIVERED IN CONNECTION WITH THE PLAN. UPON REQUEST, PEROT
                  SYSTEMS WILL PROVIDE ANY SUCH DOCUMENTS TO ANY ELIGIBLE
                  ASSOCIATE IN TANGIBLE WRITTEN FORM.





1991 Stock Option Plan           Page 8 of 10            Stock Option Agreement

<PAGE>   9
11.      Remedies. Perot Systems is entitled, in addition to any other remedies
         it may have at law or in equity, to temporary and permanent injunctive
         and otherwise equitable relief to enforce the provisions of this
         Agreement. ANY ACTION TO ENFORCE THE PROVISIONS OF, OR OTHER RELATING
         TO, THIS AGREEMENT MAY BE BROUGHT IN THE STATE OR FEDERAL COURTS HAVING
         JURISDICTION IN DALLAS, DALLAS COUNTY, TEXAS. BY SIGNING THIS
         AGREEMENT, PARTICIPANT CONSENTS TO THE PERSONAL JURISDICTION OF SUCH
         COURTS IN ANY SUCH ACTION.

12.      Assignment. This Agreement shall inure to the benefit of and be binding
         upon the parties hereto and their respective heirs, personal
         representatives, successors, and assigns. However, Participant does not
         have the power or right to assign this Agreement without the prior
         written consent of Perot Systems.

13.      Attorneys' Fees. If any legal proceeding is brought to enforce or
         interpret the terms of this Agreement, the prevailing party will be
         entitled to reasonable attorneys' fees, costs, and necessary
         disbursements in addition to any other relief to which that party may
         be entitled.

14.      Severability. If any provision of this Agreement is held invalid or
         unenforceable for any reason, the validity and enforceability of all
         other provisions of this Agreement will not be affected.

15.      Headings. The section headings used herein are for reference and
         convenience only and do not affect the interpretation of this
         Agreement.

16.      Governing Law. This Agreement shall be governed by and construed in
         accordance with the law of the State of Texas, without regard to the
         choice of law rules in such law.

17.      Entire Agreement. This Agreement, together with the Plan and any
         procedure adopted by the Committee thereunder, constitutes the entire
         agreement between the parties with respect to its subject matter and
         may be waived or modified only in writing.

18.      Changes in Capitalization. If any change is made in the Common Stock
         (including, but not limited to, changes resulting from a stock
         dividend, stock split, merger, consolidation, reorganization,
         recapitalization, exchange of shares, change in corporate structure or
         other transaction not involving the receipt of consideration by Perot
         Systems), the Committee will equitably adjust the number of shares of
         Common Stock and the Exercise Price for those shares that are subject
         to outstanding rights under this Agreement to preserve the rights of
         Participant under this Agreement. The determination of the Committee
         with respect to any such adjustments shall be final, binding and
         conclusive.

19.      No Guarantee of Continued Employment. Participant acknowledges and
         agrees that the Vesting of shares of Common Stock under this Agreement
         is earned only while continuing service to the Company as an employee
         at the will of the Company (and not through the act of being hired,
         being granted an Option or purchasing shares under this Agreement).
         Participant further acknowledges and agrees that this Agreement, the
         transactions contemplated hereunder and the Vesting schedule set forth
         herein do not constitute an express or implied promise of continued
         employment by the Company for the Vesting Period, for any period, or at
         all, and shall not





1991 Stock Option Plan           Page 9 of 10            Stock Option Agreement

<PAGE>   10
         interfere with Participant's right or the Company's right to terminate
         Participant's employment relationship with the Company at any time,
         with or without cause.





1991 Stock Option Plan          Page 10 of 10            Stock Option Agreement