Stabilization by an estimated state controller of nonlinear time-varying systems
-
Hanen Damak
and
Mohamed Ali Hammami
Abstract
In linear systems, it is well known that any combination of stabilizing state feedback controller and a state observer results in the output feedback controller which asymptotically stabilizes the closed-loop system. This is known as the separation principle, which does not generally hold for nonlinear systems. For nonlinear systems, the output feedback problem is usually pursued by extending the results of observer synthesis, which itself is a challenging problem. In this paper, we investigate the stabilization via an observer configuration problem for some classes of nonlinear time-varying systems by using new integral inequalities of Gronwall type. Given that the sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimated state feedback from the proposed practical observer will achieve the global practical exponential stabilization. Furthermore, the effectiveness of the proposed scheme is shown through simulation for two numerical examples.
Acknowledgements
The authors would like to thank the editor and the anonymous reviewers for valuable comments and suggestions, which allowed us to improve the paper.
References
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Articles in the same Issue
- Frontmatter
- Existence and uniqueness of solutions to higher order fractional partial differential equations with purely integral conditions
- Stabilization by an estimated state controller of nonlinear time-varying systems
- Global existence and blow-up of solutions for coupled bi-harmonic nonlinear wave equations
- Consequences of Srinivasa Ramanujan integrals involving Meijer’s G-function
- Parameterized Simpson-like inequalities for differential s-convex functions
Articles in the same Issue
- Frontmatter
- Existence and uniqueness of solutions to higher order fractional partial differential equations with purely integral conditions
- Stabilization by an estimated state controller of nonlinear time-varying systems
- Global existence and blow-up of solutions for coupled bi-harmonic nonlinear wave equations
- Consequences of Srinivasa Ramanujan integrals involving Meijer’s G-function
- Parameterized Simpson-like inequalities for differential s-convex functions
