高階—すなわち最大の時間間隔が一周期よりも長い—行列方程式も、区分行列に関する一階の形の方程式に変換すれば、解くことができて、それらの安定性を調べることができる。例えば、n-成分変数ベクトル x と n-次係数行列 A, B を持つ二階方程式  は n-次単位行列 I と n-次零行列 O を用いて  の形にまとめることができる。これを、現在時点とその一つ前の時点における変数をひとまとめにした 2n 成分変数ベクトル zₜ と 2n-次正方区分行列 L に関する一階方程式と見れば、既にみたように解  が得られるというわけである。ゆえに以前と同じように、このまとめられた方程式、したがってもとの二階方程式が安定となるための必要十分条件として、行列 L の任意の固有値が絶対値に関して 1 より小さいこと、を挙げることができる。
n-次元ベクトルの成す系  から一つの状態変数、具体的に y₁ に関する力学系に展開することができる。上で見た方程式のベクトル解 yₜ を A の n 個の固有値に関して展開して、それを y1,ₜ と書けば、それは y₁ の発展を記述するものであって、それ自身もまた同じ固有値を含む解を持つ。この記述は、直観的には y₁ の発展の方程式  を動機づける。ここに各パラメータ aᵢ は A の固有方程式  の係数である。すなわち、n-次元一階線型系の変数ベクトルの各成分スカラーは、各々個別の一スカラー変数 n-階差分方程式に従って発展する。そのような一変数方程式の安定性はもとの行列差分方程式の安定性と同じである。
On February 1, 2009, Stefan F. Cook, a Major in the United States Army Reserve, contacted Taitz via e-mail, asking to be part of her lawsuit. On May 8, he volunteered to serve for one year in Afghanistan beginning on July 15, 2009. The Army accepted his offer and ordered him to report on that date. On July 8, however, he filed suit, with Taitz as his lawyer, seeking a temporary restraining order and status as a conscientious objector, arguing that his deployment orders were invalid because Obama was not a natural-born U.S. citizen, and therefore ineligible to serve as commander-in-chief of the armed forces. His orders were thereupon revoked; an Army spokesperson stated, "A reserve soldier who volunteers for an active duty tour may ask for a revocation of orders up until the day he is scheduled to report for active duty." Accordingly, Cook's case was dismissed as moot on July 16.In the lawsuit, captioned Stefan Frederick Cook v. Wanda L. Good and filed in the United States District Court for the Middle District of Georgia, Cook asserted that he "would be acting in violation of international law by engaging in military actions outside the United States under this President's command. ... simultaneously subjecting himself to possible prosecution as a war criminal by the faithful execution of these duties." In April, before Cook volunteered for deployment to Afghanistan, he had been included in Taitz's list of people she said she represented as plaintiffs, in a letter raising the citizenship issue. A retired Army major general and an active reserve US Air Force lieutenant colonel subsequently joined the Georgia case as plaintiffs alongside Cook. Cook's deployment orders were canceled, and a government spokesman explained, "The Commanding General of SOCCENT (U.S. Special Operations Central Command) has determined that he does not want the services of Major Cook, and has revoked his deployment orders." An Army CENTCOM spokesman rejected as false claims that the revocation validated Cook's claims: "This in no way validates any of the outlandish claims made by Maj. Cook or his attorney. The idea that this validates those charges about the president's fitness for office is simply false."After the case was filed, Taitz alleged that Cook had been terminated from his civilian job with a defense contractor, after the situation at his company had become "nutty and crazy".Cook received significant media coverage on July 16, 2009, from Fox News's Sean Hannity. Hannity said in his second of two reports:We told you Tuesday about an Army reserve soldier who challenged his deployment orders on the grounds that President Obama has not proven he is a U.S. citizen. Major Stefan Frederick Cook, who was supposed to deploy to Afghanistan in the coming days, has had his orders revoked. According to his lawyer, "They just said 'order revoked.' No explanation. No reasons. Just revoked." Major Cook and his lawyer expressed joy at this outcome and took it as an admission on the part of the military that the president is not in fact a legitimate citizen by birth.Hannity was criticized for publicizing the "birthers" movement. News Hounds wrote:Fox News had added legitimacy to the irrational and baseless conspiracy-theorist "birthers" who continue to insist, despite evidence to the contrary, that Barack Obama was not born in the United States and [is] thus an illegitimate president. One such effort came from Sean Hannity, reporting on a soldier challenging his deployment to Afghanistan on the grounds that Obama is not eligible to be president. Hannity had failed to note in his report the availability of Obama's birth certificate and how the birther claims have been completely investigated and debunked. Hannity gave an update to the Afghanistan story last night (7/15/09) and took it a step further by suggesting, along with the plaintiff, that the subsequent revocation of the soldiers [sic] deployment orders indicated that his allegations were proved true. But Hannity omitted key details that point to a scam by the soldier. ... Had Hannity bothered to do the simplest of Google searches, he would have also uncovered this key piece of information from that day's Georgia Ledger-Enquirer [sic] newspaper.... So, Maj. Cook filed a request to serve the Commander-in-Chief in Afghanistan on May 8, well after Obama had assumed the presidency, but now, about two months later, is claiming that Obama is not qualified to be president. And instead of going through the administrative process to revoke his orders, which would seem to be a pro forma matter, he sued in federal court.—News Hounds, citing The Ledger-EnquirerAfter the lawsuit was reported in the Columbus Ledger-Enquirer, the newspaper reported receiving "the highest volume of traffic ever by a single story in the history of ledger-enquirer.com, including written threats against the newspaper", with nearly half a million new readers and hundreds of e-mails. The threats prompted an increase in security around the courthouse where Cook's case was heard, as well as precautions being taken to protect the author of the newspaper's reports on the case. Executive Editor Ben Holden noted: "The chatter had the feel of a righteous cause – almost a religious cause – because some people hate this president."