If an operating region is divided into a number of sectors and if it is shown that the system is stable in equilibrium point corresponding to each of the sectors, can it be said that the system is asymptotically stable in the entire operating region consisting of each of these sectors? Is there any theorem that can be cited to reinforce the premise?
I associate it with multiple stable states, and in the event of a disturbance, with the possibility of jumping from one state to another. Such a system will be asymptotically stable, but will it be predictable? In addition, it is difficult to imagine such a system where all states are stable. Oscillations and chotic behaviors are also possible in such systems.
Hi
In theory i suppose everything is correct and stable parts make stable process. Yet, in practice more precise observation is needed and you have to see whether it is constant during the whole process or not. By testing and analysing our data and comparing results for many times.
Hi
In theory i suppose everything is correct and stable parts make stable process. Yet, in practice more precise observation is needed and you have to see whether it is constant during the whole process or not. By testing and analysing our data and comparing results for many times.
Comments on the stability can only be given if the Lebesgue measure at the point of discontinuity is zero that means there are finite points of discontinuities at the junction points of two regions. These cases normally appear for bilinear and weakly linear systems. So while commenting on the stability, all the connecting points joining all the regions should be considered.
@Jagannath, how to ensure that the Lebesgue measure at the point of discontinuity i.e. at junction points of two regions is zero? Is there any theorem for that? What are the necessary assumptions that need to be made to ensure that? Are you referring to " Lebesgue’s Criterion for Riemann integrability "? Can u please pinpoint some references that I could use for getting deeper insights into it?
Thanks !!!!
Biswajit Debnath Please send me your problem I will try to check the complete stability and get back to you. I got through the concepts from measure theory book and relate to mathematical control on my own. I am sorry I don't have any references to send you. It is my understanding only.
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