Abstract
This paper investigates the adaptive parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems of a class of nonlinear descriptor systems via dissipative matrix method. Firstly, under an output feedback law, two nonlinear descriptor systems are transformed into two nonlinear differential-algebraic systems by nonsingular transformations, and a sufficient condition of impulse-free is given for two resulting closed-loop systems. Then, the two systems are combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique. Based on the dissipative system, an adaptive parallel simultaneous stabilization controller and a robust adaptive parallel simultaneous stabilization controller are designed for the two systems. Furthermore, the case of more than two nonlinear descriptor systems is investigated. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the adaptive parallel simultaneous stabilization controllers obtained in this paper work very well.
Highlights
In practical control designs, a commonly encountered problem is to design feedback controller(s) to stabilize a given family of parallel systems
The resulting closed-loop system which consists of an individual system and its corresponding controller via its state or output feedback based on that control law is asymptotically stable
This paper has investigated the adaptive parallel simultaneous stabilization problems of a class of nonlinear descriptor systems via dissipative matrix method
Summary
A commonly encountered problem is to design feedback controller(s) to stabilize a given family of parallel systems. For the case in which the singular matrix Ei = Mi diag{Ir, 0}Mi with Mi being an orthogonal matrix, the parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems were, respectively, studied in [1, 18] for two or a family of nonlinear descriptor systems via the Hamiltonian function method. In this paper, motivated by the Hamiltonian function method [2, 19,20,21,22,23,24,25,26,27,28,29], we apply the structural properties of dissipative matrices to investigate the adaptive parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems for a class of NDSs via output feedback law [30, 31], and propose a new approach, called the dissipative matrix method, to study NDSs. Firstly, under an output feedback law, two NDSs are transformed into two nonlinear differential-algebraic systems by nonsingular transformations, and a sufficient condition of impulse-free is given for two closed-loop systems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
