Psalm 7 is not penitential. Neither is Psalm 8. They are included here in this post and the next because they form a sequence along with Psalm 6, which is considered penitential. (Link to Psalm 8)
Recap:
1. Psalm 1. Introduction to the Psalter. God favors the righteous; the unrighteous will perish. God defines righteousness.
2. Psalm 2. Introduction to the Royal Family; the King is appointed
3. Psalm 3. The King appears as a man on earth
4. Psalm 4. The King on earth walks in righteousness but has many enemies who do not receive him
5. Psalm 5. The King prays Psalm 1
6. Psalm 6. The King is assaulted by enemies and feels assaulted by God; he cries out to the Lord for deliverance
And, moving forward:
7. Psalm 7. The King addresses accusations against himself; war is fully declared and victory won
8. Psalm 8. First denouement, a day of rest, the end of the story foretold, a post-resurrection view, creation celebrated
Explanation
“Early Christian writers adapted prosopological analysis for interpreting poetic biblical texts like the Psalms and the Song of Songs, and routinely identified the speaking “I” (ego) of the Psalms as Christ.” —Michael Cameron, 171
The key to understanding the Psalter is Jesus Christ. When the reader perceives Christ in the first person speaking role of the Psalms of David, much of what otherwise may appear to be a scattered jumble of statements falls into place. My premise is that “the man,” of Psalm 1 describes Christ in particular. The immediately following psalms unfold as in the Recap and Moving Forward above. When the superscriptions assign a psalm to David, David is “taking on” the persona of someone else–the Christ. (See Peter’s statements in Acts 2:29-31.) A good Greek term to describe this rhetorical tool is prosopopoeia. (1)
In these first several psalms we find a progression from God’s decree in heaven (Psalm 2:6-9 and especially verse 7, “the ordinance of the Lord” LXE) to its enactment on earth. The entire sequence is the Gospel of Christ our King. He was appointed by God in eons past to be Savior and Sovereign Lord of humanity. He performed the salvation by means of his incarnation, substitutionary death on the cross, his resurrection, and ascension. The Psalter records in advance Christ’s holy ministry. Much of this is presented through first person prayers and other speech. In the recorded prayers, as the Apostle Paul writes, “…we have the mind of Christ” (1Co 2:16b ESV). 
When the reader adheres to the simplicity of this key concept of interpretation, the love of God for his Son all but shouts from the pages of the Psalter. When we see that love of the Father/Son Godhead and ourselves as readers interacting spiritually with the text by means of the indwelling Holy Spirit, we are included in the fellowship of love of Father, Son, and Holy Spirit in an interactive way. When we hear Christ speaking the psalms, the love of God for us pours into our hearts. It is a transforming love, “… God’s love has been poured into our hearts through the Holy Spirit who has been given to us” (Rom 5:5b ESV).
Psalm 7
Following the progressive sequence from Psalm 1 through Psalm 8, Psalm 7 moves beyond Psalm 6. In Psalm 6, the human Son-of-God-King presents himself in weakness and, possibly, what we might experience as confusion, if this were happening to us. God seems to be angry with him and is far away. The beleaguered Son/King continually cries to the Lord as death draws nearer. Eventually, God does answer. Although Psalm 6 is called the first of the Penitential Psalms, in it the psalmist does not confess any sins. Neither does God offer forgiveness when he answers the psalmist’s prayer. The reader should keep this fact well in mind as she reads through the remainder of the penitential psalms. Any sin expressed will not be the sin of the Son, but of those he represents.
Psalm 7 is blatantly defensive. The accusations from the speaker’s enemies have been pinpointed (vv 3-4), and the psalmist vehemently denies any wrongdoing on his part by asking God to punish him if indeed he committed the crimes stated by his accusers (vv 4b-5). He then appeals to God on the basis of God’s decree, which is recorded in Psalm 2. In other words, he prays Psalm 2 as concerns himself. Psalm 2:6-9 shows God decreeing Christ as King (quoted in Hebrews 1:5). Psalm 7:6-16 speak of the decreed judgment upon those who reject God and his appointed Ruler. (See also Psalm 1:4-6.)
Verses 7-8a of Psalm 7 in the Septuagint makes better sense when heard as spoken by the Chorus, which is slightly off-stage but ever present. (See the dramatic setting including the Chorus in “Penitential Psalms: The Amazing Psalm 6–Windup to the Pitch“.)
And the congregation of the nations shall compass thee: and for this cause do thou return on high. The Lord shall judge the nations. (Psalm 7:7-8a LXE)
Verses 7-8a are embedded solidly within a paragraph of verses clearly spoken by the main speaker of Psalm 7, yet verse 7 appears to be addressing Christ the Lord, rather than God most High, and verse 8a is about the Lord. Use of a chorus explains this anomaly. We learn from New Testament Scripture, Isaiah, and other Psalms that “the nations” shall gather around Christ the King, and it is Christ who shall “return on high,” in other words–ascend–after his resurrection, in order for his Lordship over the nations to begin. It also befits a dramatic production to assign the speech in verse 7 about “the congregation” to the Chorus. Verses 14-16 are also suited as lines for the Chorus. If 14-16 are spoken by the Chorus, then verse 17 is the closing “Amen” of thanksgiving spoken once more by the main speaker of Psalm 7.
Who is this God on High who wreaks vengeance upon those who oppose his favored Son/King? Is he being unfair, autocratic, authoritarian, narrow, and fascist in his outlook?
First, God is Creator. At this point in human history, that fact cannot be changed. It follows from this fact that God is Sovereign. Whether we as people like it or not, the Creator is the Ruler.
But secondly, he is a God who gives many chances.
Now therefore understand, ye kings: be instructed, all ye that judge the earth. 11 Serve the Lord with fear, and rejoice in him with trembling. 12 Accept correction, lest at any time the Lord be angry, and ye should perish from the righteous way: whensoever his wrath shall be suddenly kindled, blessed are all they that trust in him. (Psalm 2:10 LXE)
Psalm 7 reinforces the call of God to repentance found above in Psalm 2.
God is a righteous judge, and strong, and patient, not inflicting vengeance every day. 12 If ye will not repent, he will furbish his sword; he has bent his bow, and made it ready. (Psalm 7:11 LXE)
Verses 14-16 work well as a choral commentary upon the preceding four verses. These lines speak of an unnamed “he,” which from the context can only be the unrighteous false accuser of the righteous King. They spell out the bad choice the unrighteous one made and how he is bringing down upon his own head his just retribution. These verses demonstrate the false reasoning of those who blame God for condemning evil. Here the just punishment that pursues the unrighteous is nothing more than what that person planned for an innocent person who had done him no wrong. God is patient and just, inviting sinners to repent.
Verse 8a says, “The Lord shall judge the nations…” Immediately the Judge, when not yet the Judge but still the suffering Savior, in response to God on account of the words just spoken by the chorus, pleads with God, “Judge me, O Lord,…” The righteous Judge wants to be judged by God first.
And God does acquit him. Psalm 7 ends very strongly, much as Psalm 2. The righteous King is vindicated, and his false accuser falls into the pit his own hands have dug (vv 15-16). These words of Scripture have been written in future tense, as prophetic, yet their outcome is secure.
From Psalms 3 through 6, the audience perceives the King descending, as he falls deeper and deeper into persecution and human vulnerability. Psalm 7 presents him rising up in strength to face his accuser, along with the announcement of his final victory. Then Psalm 8 comes crashing onto the scene in a wild exuberance of joyful praise. I’ll give Psalm 8 a posting of its own.
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1 We encounter this ancient tool of figurative language called prosopopoeia nearly every day. Whenever we hear a child or someone else speak “Valley talk” as they describe an encounter with another person, we might hear a statement such as, “And then she’s like, ‘………’.” What transpires in the elipsis, the dots in the quotation, is a perfect reenactment of the described person’s words, intonation, mannerisms, and attitude, albeit exaggerated for effect. This is prosopopoeia, when a speaker or writer takes up the persona of someone else and becomes them imitatively. This is what acting on stage is all about. Real life actors take up the lives and characters of others in order to portray them with convincing reality. Within Psalms, David, the prophet/actor being used by God, takes up the persona of the Christ. Who has a greater role in God’s plan of salvation: David the man or Christ the Atoning King? Did David know that he was being used by God this way? According to Peter in Acts 2:30-31, David did know that he was prophesying about Another.