Observer and descriptor satisfying incremental quadratic constraint for class of chaotic systems and its applications in a quadrotor chaotic system

• Published in: Chaos, solitons and fractals Vol. 137; p. 109874
• Main Authors: Sabir, Muhammad, Marwan, Muhammad, Ahmad, Salman, Fiaz, Muhammad, Khan, Farhan
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 01.08.2020
• Subjects: Chaotic system; Incremental quadratic constraints; Linear Matrix Inequalities; Observer design; Robotics; Secure communication; Synchronization; Incremental quadratic constraints; Chaotic system; Linear Matrix Inequalities; Secure communication; Synchronization; Robotics; Observer design
• ISSN: 0960-0779; 1873-2887; 1873-2887; 0960-0779
• DOI: 10.1016/j.chaos.2020.109874

•Nonlinear chaotic system is transformed into observer designed in our work.•Calculate the Incremental Quadratic matrix for nonlinear function using algorithm given by Zhao [34].•Use adaptation law (23) to assure negative deniteness of energy function as adaptive observers approach to original parameters.•Use concept of Linear Matrix Inequalities to determine gain matrices with suitable dimension.•A grey scaled image is considered for image transmission from transmitter to receiver end.•A circuit is designed and implemented into robot to determine dynamics of aerial robot in rectangular region. A drone based on four rotors is considered in this research paper. Its chaotic solution is shown bounded in an inscribed sphere whose vertices are tangent to faces of octahedron. Based on concept of constrained optimization; Linear Matrix Inequalities (LMIs) satisfying quadratic constraint increment multiplier matrix σm, state observers and descriptors with estimated parameter is calculated. Moreover, an image file is decrypted by designing description for mentioned chaotic system and then encrypted on its receiver end. Furthermore, an electric circuit is designed for chaotic quadrotor using LTspice and is fitted into wireless flying robot to observe its dynamics in bounded rectangular region.