scholarly journals Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems

2011 ◽  
Vol 136 (2) ◽  
pp. 185-194 ◽  
Author(s):  
Volker Reitmann
Keyword(s):  
Input Output ◽  
Realization Theory ◽  
Infinite Dimensional ◽  
Stability Investigation ◽  
The Stability

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

$H^2 $-Functions and Infinite-Dimensional Realization Theory

1975 ◽  
Vol 13 (1) ◽  
pp. 221-241 ◽  
Author(s):  
J. S. Baras ◽  
R. W. Brockett
Keyword(s):  
Realization Theory ◽  
Infinite Dimensional

scholarly journals Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Xiaohui Xu ◽  
Xiaofeng Yin ◽  
Jiye Zhang ◽  
Peng Wang
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Stochastic Disturbances ◽  
Infinite Dimensional ◽  
Disturbance Propagation ◽  
Vector Lyapunov Function ◽  
Look Ahead ◽  
The Stability

Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.

Infinite Dimensional Linear Realization Theory

1982 ◽  
Vol 29 (3) ◽  
pp. 287-308
Author(s):  
M. J. CHAPMAN ◽  
A. J. PRITCHARD
Keyword(s):  
Realization Theory ◽  
Infinite Dimensional

Weyl's theorem for the square of operator and perturbations

2015 ◽  
Vol 17 (05) ◽  
pp. 1450042
Author(s):  
Weijuan Shi ◽  
Xiaohong Cao
Keyword(s):  
Hilbert Space ◽  
Compact Operator ◽  
Complex Hilbert Space ◽  
Linear Operators ◽  
Weyl’S Theorem ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Weyl Spectrum ◽  
The Stability

Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. T ∈ B(H) satisfies Weyl's theorem if σ(T)\σw(T) = π00(T), where σ(T) and σw(T) denote the spectrum and the Weyl spectrum of T, respectively, π00(T) = {λ ∈ iso σ(T) : 0 < dim N(T - λI) < ∞}. T ∈ B(H) is said to have the stability of Weyl's theorem if T + K satisfies Weyl's theorem for all compact operator K ∈ B(H). In this paper, we characterize the operator T on H satisfying the stability of Weyl's theorem holds for T2.

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