NCS - 15 - Lyapunov stability - Definition and explanation

This lecture explains the concept of Lyapunov stability. For linear systems, BIBO stability and Internal stability are widely studies. For nonlinear systems, Lyapunov stability is more widely studies. Furthermore, for nonlinear systems, we talk about stability of equilibrium points rather than stability of systems. For linear systems, blowing up of states is equivalent to instability, however, for nonlinear systems, blowing up is only one form of instability.

[@sandfordstebbings125]

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.

[@anneoni691]

Thank you professor Farooqi for the easy explanation of epsilon delta argument.

[@mzakirbaig]

Such a nice and clear explanation. Very unique video for Control Students. Appreciated and Jazakallah Sir

[@MAFarooqi]

Thanks.

[@GauravKumar-np2qm]

Thanks for uploading this video.

[@akiryanafans6997]

Very well explained, more such videos are welcome

[@gauffreb4529]

Than kyou gor these clear explanations !

[@AtulKumar-xf3sl]

Please send some articles for lyapunov stability to check the system

[@mutiur7396]

Why is delta function of epsilon in Lyapunov Stability mathematical equation? What is it significance although you just considered it as a number.

[@user-mb6pr7yl3g]

Salam Dr
Thank you for these lectures.
Please may get the file of Matlab example.

[@arunbali7480]

Good evening sir
What is the definition of Semi-globally uniformly ultimately bounded?

[@MAFarooqi]

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.

[@arunbali7480]

@@MAFarooqi Thanks sir for nice explanation.
But what about Semi-globally uniformly ultimately bounded?

[@Annunni3]

very good explanation! how do we calculate eplison and delta ?

[@MAFarooqi]

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.

[@Annunni3]

@@MAFarooqi Thank you for the answer.