Is there an equivalent of the Khalil's Nonlinear Systems for discrete-time systems?
I am particularly interested in matters of advanced stability analysis, perturbed systems, singular perturbation theory.
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Rodrigo de Azevedo
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shnnnms
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Forced or unforced? – Rodrigo de Azevedo Aug 09 '21 at 13:46
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preferably both – shnnnms Aug 09 '21 at 14:19
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I have been looking for a discrete-time version of Khalil's Nonlinear Systems book but haven't been able to find anything. The closest thing I could find to cover the topics of Khalil is using these three references:
"Lyapunov Theory for Discrete Time Systems", https://arxiv.org/pdf/1809.05289.pdf This is a report that contains Lyapunov stability results.
"Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach" by Wassim M. Haddad, and VijaySekhar Chellaboina. Chapter 13 has Lyapunov stability and Dissipativity results. Chapter 14 has optimal nonlinear control.
"Stochastic Approximation, A Dynamic Systems Viewpoint" by Vivek Borkar. If you ignore the stochastic elements, the book relates a discrete-time system to a continuous-time system. Then using the results for continuous-time systems you can conclude results for the discrete time system. Chapter 6 has results for two-time scale systems.
If you know any other books/papers that have useful results not covered by these references I would like to add them to the collection.
dgadjov
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There is also this interesting article for singular perturbation analysis in discrete-time systems: link – shnnnms Aug 28 '21 at 19:29