Augustine. Exposition on the Book of Psalms. Schaff, Philip (editor). New York: Christian Literature Publishing Co, 1886. Nicene and Post-Nicene Church Fathers: Series 1: Volume VIII. Re-published 2014, Catholic Way Publishing. Kindle electronic edition, ISBN-13: 978-1-78379-372-3.
Augustine observes the type of praise given in Psalm 145:1 is appropriate to be given to God. He therefore takes the reference to David to speak allegorically of Christ (Augustine Psalms, loc. 342539, par. 1). The praise is due to God every day forever (v. 2).
Psalm 145speaks of the scope of God's praise. Augustine observes that it is limitless, according to verses 3-4. It is neither bounded by space or time, but extends everywhere and throughout all generations (Augustine Psalms, loc. 342554, par. 3).
Verses 5-7 speak to the content of the praise due to God - his works and his character (Augustine Psalms, loc. 342569, par. 4). The worship of God rightly focuses on God, not on anything in the created order. Augustine describes the praise to God as a means of growing in understanding and experiencing God's blessings (Augustine Psalms, loc. 342584, par. 5).
Verses 8-9 speak of God's mercy and compassion. Augustine asks what we actually deserve, especially those who have despised God (Augustine Psalms, loc. 342589, par. 7). Yet he recognizes that God's mercy brings his gracious compassion to all those who turn to him. God is severe against those who reject him but merciful to those who hope in him (Augustine Psalms, loc. 342604, par. 8). Augustine continues by elaborating on the order of all creation, by which all creatures, according to their nature and ability, give the appropriate honor to God. This is often by showing their beauty or their usefulness (Augustine Psalms, loc. 342635, par. 11).
Verse 14 cndidly admits that godly people fall. Sometimes it is into poverty, sometimes into some other shame. But in all thins the Lord strengthens them (Augustine Psalms, loc. 342659, par. 13). At the right time, though not always when we first desire, God gives his people their needed food and blesses them (vv. 15-16). Verse 17 describes this as God's righteousness at work.
Those who call on God find he is near (v. 18). Augustine does note that the call on God must be in truth, not an effort to manipulate God (Augustine Psalms, loc. 342679, par. 16). God gives us what is good. In turn, we praise him. This adjusts our will so that, in verse 19, we find God gives us what we desire (Augustine Psalms, loc. 342689, par. 17).
In the end, in verses 20-21, God rewards the righteous and punishes sinners.