Analysis of fast-sampled non-linear systems: generalised frequency response functions for δ-operator models

Analysis of Nonlinear Systems with Stochastic Input and Stochastic Parameters—II

Theory of nonlinear systems

The identification of block-oriented systems represented by interconnections of linear dynamic systems and non-memory nonlinear elements have been of great importance for control and for analysis of biological nonlinear systems. In this study, two new algorithms to obtain structural models of nonlinear systems using numerically-given (experimentally obtained) Volterra kernels are proposed. One is to determine the parallel factorable base model; a sum of subsets, each of which has a parallel structure of linear dynamic systems whose outputs are multiplied. Another is called the Sm model; linear dynamic systems and nonlinear power elements in cascade. The results of numerical experiments showed that both methods could be practically useful for identifications and analysis of nonlinear systems.

On the application of diakoptics to nonlinear systems

Nonlinear [formula omitted]-gain verification for nonlinear systems

As we all know, many biological and physical systems, such as neuronal systems and disease systems, are featured by certain nonlinear and complex patterns in their elements and networks. These phenomena carry significant biological and physical information and regulate down-stream mechanism in many instances. This issue of Discrete and Continuous Dynamical Systems, Series S, comprises a collection of recent works in the general area of nonlinear differential equations and dynamical systems, and related applications in mathematical biology and engineering. The common themes of this issue include theoretical analysis, mathematical models, computational and statistical methods on dynamical systems and differential equations, as well as applications in fields of neurodynamics, biology, and engineering etc. <br>&nbsp; &nbsp Research articles contributed to this issue explore a large variety of topics and present many of the advances in the field of differential equations, dynamical systems and mathematical modeling, with emphasis on newly developed theory and techniques on analysis of nonlinear systems, as well as applications in natural science and engineering. These contributions not only present valuable new results, ideas and techniques in nonlinear systems, but also formulate a few open questions which may stimulate further study in this area. We would like to thank the authors for their excellent contributions, the referees for their tireless efforts in reviewing the manuscripts and making suggestions, and the chief editors of DCDS-S for making this issue possible. We hope that these works will help the readers and researchers to understand and make future progress in the field of nonlinear analysis and mathematical modeling.

Practical stability analysis and synthesis for nonlinear singular systems .- 3 Strongly absolute stability analysis for Lur'e singular .- 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems. 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems.

Theory of nonlinear control

A state-space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed. The robustness of a class of nonlinear systems subject to L/sub 2/-bounded structured uncertainties is characterized in terms of a nonlinear matrix inequality (NLMI), which yields a convex feasibility problem. As in the linear case, scalings are used to find a Lyapunov or storage function that give sufficient conditions for robust stability and performances. Sufficient conditions for the solvability of robustness synthesis problems are represented in terms of NLMIs as well. With the proposed NLMI characterizations, it is shown that the computation needed for robustness analysis and synthesis is not more difficult than that for checking Lyapunov stability; the numerical solutions for robustness problems are approximated by the use of finite element methods or finite difference schemes, and the computations are reduced to solving linear matrix inequalities. Unfortunately, while the development in this paper parallels the corresponding linear theory, the resulting computational consequences are, of course, not as favourable.

A copula-based Gaussian mixture closure method for stochastic response of nonlinear dynamic systems

We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems.

Output frequency response function-based analysis for nonlinear Volterra systems

A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables

Enhanced robust stability analysis of large hydraulic control systems via a bifurcation-based procedure

In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS) was proposed by Okubo (1985). In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k))║≤α + β║v (k)║^γ , where α≥0, β≥0, 0≤γ≤1. When 0≤γ<1. It is easy to extend the method to discrete time systems. But in the case γ = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.