Abstract
This paper investigates the problem of stability analysis and observer design for nonlinear descriptor systems with time-varying delay. In the systems, the nonlinear function satisfies the one-sided Lipschitz condition and the quadratic internal boundary condition. The disturbance is considered in both the state and the output equation. Using one-sided Lipschitz condition, the quadratic internal boundary condition, and the generalized Lyapunov method, we establish the non-strict bilinear matrix inequality (BMI)-based condition. We change the condition into strict bilinear matrix inequality (BMI) condition. Furthermore, we give the linear matrix inequality-based condition to ensure the gradual convergence of state estimation error and to accomplish robustness against L2 norm bounded disturbances by utilizing change of variables for straight forward computation of the observer gain matrix. Finally, a numerical example is given to verify the effectiveness of the observer design scheme.
Highlights
Descriptor systems, known as singular systems, implicit systems or generalized state space systems, are widely used in many fields
Using the one-sided Lipschitz condition, the quadratic internal boundary conditions, and the generalized Lyapunov method, first, we propose a non-strict bilinear matrix inequality (BMI)-based condition, which is further transformed into strict 10:1 (2018)
We develop the linear matrix inequality (LMI)-based condition to ensure asymptotic convergence of the state estimation error to origin and to accomplish robustness against L2 norm bounded disturbances
Summary
Descriptor systems, known as singular systems, implicit systems or generalized state space systems, are widely used in many fields. In [7], Liu et al investigated state observer design problem for a class of nonlinear dynamical systems with interval time-varying delay that satisfies the one-sided Lipschitz condition. Many research results have been reported in the literature [12,13,14,15] None of these observer design schemes can be applied to the one-sided Lipschitz descriptor systems with time-varying delay. A novel observer design method is proposed for the one-sided Lipschitz descriptor system with time delay. Using the one-sided Lipschitz condition, the quadratic internal boundary conditions, and the generalized Lyapunov method, first, we propose a non-strict bilinear matrix inequality (BMI)-based condition, which is further transformed into strict.
Sign-in/Register to view highlights & summary 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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
