Nonlinear Systems Analysis

@article{Vidyasagar1980NonlinearSA,
  title={Nonlinear Systems Analysis},
  author={Mathukumalli Vidyasagar and Charles A. Desoer},
  journal={IEEE Transactions on Systems, Man, and Cybernetics},
  year={1980},
  volume={10},
  pages={537-538}
}
Introduction. Non-linear Differential Equations. Second-Order Systems. Approximate Analysis Methods. Lyapunov Stability. Input-Output Stability. Differential Geometric Methods. Appendices: Prevalence of Differential Equations with Unique Solutions, Proof of the Kalman-Yacubovitch Lemma and Proof of the Frobenius Theorem. 
Lyapunov stability for discontinuous systems
The present work studies the stability analysis of equilibrium of ordinary differential equations with the discontinuous right side, also called discontinuous differential equations, using the notion
On stability of linear systems with time-varying delay: generalized Lyapunov equation
  • R. Yu
  • Mathematics
    1999 IEEE Africon. 5th Africon Conference in Africa (Cat. No.99CH36342)
  • 1999
This paper presents some delay independent stability criteria for linear systems with time-varying delay. The main result is stated in terms of the so-called generalized Lyapunov equation.
Reduced-order controller design for stabilization of Lipschitz nonlinear systems
The global asymptotic stabilization is discussed for the MIMO Lipschitz nonlinear systems whose free dynamics are Lyapunov stable. Sufficient condition for constructing reduced-order dynamic output
ASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS
This paper deals with stability of time-varying differential equations. New asymptotic stability conditions for time-varying continuous systems with more general assumptions are given. The Gronwall's
On the stability of time-varying differential equations *
This paper deals with stability of time-varying differential equations. New asymptotic stability conditions for time-varying continuous systems with more general assumptions are given. The Gronwall's
Observer-based control for fractional-order continuous-time systems
TLDR
A generalization of Gronwall-Bellman which is proved in the appendix is used to derive the closed-loop asymptotic stability of fractional-order systems using an observer-based control law.
Nonlinear and Adaptive Control of Complex Systems
TLDR
The Faces of Complexity presents a model of nonlinear control of Multivariable Systems that combines Adaptive and Robus Control Design, and nonlinear Systems: Analysis and Design Tools, which describes the design tools used for this model.
Practical Stability of Nonlinear Time-Varying Cascade Systems
In this paper, we investigate the practical stability problem of nonlinear time-varying cascade systems. We give some sufficient conditions that guarantee practical global uniform asymptotic
Stability of Nonlinear Systems
The sections in this article are 1 Stability of Nonlinear Systems 2 Nonlinear System Preliminaries 3 Lyapunov, Orbital, and Structural Stabilities 4 Various Stability Theorems 5
...
1
2
3
4
5
...

References

Feedback systems: Input-output properties
  • D. Elliott
  • Computer Science
    Proceedings of the IEEE
  • 1976