A lot of lecturers and videos use jargon to cover their lack of understanding. I am so impressed by your explanations. Its clear, and you spend the time to explain simple concepts that people may not know. I really appreciate your lectures.
Delta can be approximated by using Lyapunov theory. We select positive definite candidate Lyapunov function and find its derivative with respect to time, the region in which V_dot is negative definite is an approximation to delta, also called region of attraction. This is explained in later lectures.
Because each epsilon has strictly only one delta associated with it. You write it down as a function because, in functions, the output is unique (i.e., You can't have two outputs for the same input). The formal definition in Slotine's book on applied nonlinear control, however, says: "for any ball of radius R, there exists "at least one" smaller ball of radius r", so I guess that contradicts what I said earlier. It depends on which reference you're reading. According to the video, just one; while according to my reference, at least one. Personally, I would go with the reference's definition.
Ultimate boundedness means that the states will ultimately enter into a bounded region ( states will ultimately become smaller than a bound). Uniform ultimate boundedness is a term relevant with non-autonomous systems (time varying systems). Behavior of non-autonomous systems, among other things, also depends upon the initial time. Therefore, uniformly ultimately bounded means that states of the system will ultimately become smaller than a bound for any initial time.
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A lot of lecturers and videos use jargon to cover their lack of understanding. I am so impressed by your explanations. Its clear, and you spend the time to explain simple concepts that people may not know. I really appreciate your lectures.
Thank you professor Farooqi for the easy explanation of epsilon delta argument.
Very well explained, more such videos are welcome
Such a nice and clear explanation. Very unique video for Control Students. Appreciated and Jazakallah Sir
Thanks.
Than kyou gor these clear explanations !
Thanks for uploading this video.
Please send some articles for lyapunov stability to check the system
Thank you sir❤
very good explanation! how do we calculate eplison and delta ?
Delta can be approximated by using Lyapunov theory.
We select positive definite candidate Lyapunov function and find its derivative with respect to time, the region in which V_dot is negative definite is an approximation to delta, also called region of attraction. This is explained in later lectures.
@@MAFarooqi Thank you for the answer.
Salam Dr
Thank you for these lectures.
Please may get the file of Matlab example.
Why is delta function of epsilon in Lyapunov Stability mathematical equation? What is it significance although you just considered it as a number.
Because each epsilon has strictly only one delta associated with it. You write it down as a function because, in functions, the output is unique (i.e., You can't have two outputs for the same input). The formal definition in Slotine's book on applied nonlinear control, however, says: "for any ball of radius R, there exists "at least one" smaller ball of radius r", so I guess that contradicts what I said earlier. It depends on which reference you're reading. According to the video, just one; while according to my reference, at least one. Personally, I would go with the reference's definition.
Good evening sir
What is the definition of Semi-globally uniformly ultimately bounded?
Ultimate boundedness means that the states will ultimately enter into a bounded region ( states will ultimately become smaller than a bound).
Uniform ultimate boundedness is a term relevant with non-autonomous systems (time varying systems). Behavior of non-autonomous systems, among other things, also depends upon the initial time. Therefore, uniformly ultimately bounded means that states of the system will ultimately become smaller than a bound for any initial time.
@@MAFarooqi Thanks sir for nice explanation.
But what about Semi-globally uniformly ultimately bounded?