Impulsive Functional Observer Design for Fractional-Order Nonlinear Systems Satisfying Incremental Quadratic Constraints

State and adaptive disturbance observer co‐design for incrementally quadratic nonlinear descriptor systems with nonlinear outputs

“…Recently, the investigation for systems satisfying 𝛿QC has yielded fruitful results. [18][19][20][21][22][23][24][25][26] In Reference 21, a technique for designing state observers for incrementally quadratic systems has been presented to address the problem of secure chaotic communication. Adaptive state observers for nonlinear systems with 𝛿QC have been put forward in References 19,20.…”

“…It is seen that most of the studies [18][19][20][21][22][23][24][25][26] on 𝛿QC mentioned above primarily focus on state observer design. However, the disturbance frequently occurs in practical engineering and can significantly impact system performance.…”

“…In other words, various types of nonlinearities can be seen as a particular case of $$$ \delta $$$QC by selecting appropriate $$$ \delta $$$MMs, such as nonlinearities satisfying monotone, 14 quadratic inequality, 16 incremental bounded sector conditions, 8,9,17 quadratic inner‐bounded conditions, 11 Lipschitz conditions, 13,15 one‐sided Lipschitz conditions 10‐12 and more. Recently, the investigation for systems satisfying $$$ \delta $$$QC has yielded fruitful results 18‐26 . In Reference 21, a technique for designing state observers for incrementally quadratic systems has been presented to address the problem of secure chaotic communication.…”

“…Adaptive state observers for nonlinear systems with $$$ \delta $$$QC have been put forward in References 19,20. The state observers have also been proposed for semi‐Markov jump systems, fractional‐order Systems, and differential inclusion systems with nonlinearities of $$$ \delta $$$QC in References 22,25,26. More importantly, there have also been a few results 18,23 applying to $$$ \delta $$$QC to descriptor systems.…”