Negative imaginariness and positive realness analysis of state-space symmetric systems with interval uncertainty

2021 ◽  
pp. 095965182110480
Author(s):  
Mei Liu ◽  
Hong Lin ◽  
Yan Wang ◽  
Gang Chen
Keyword(s):  
State Space ◽  
Interval Uncertainty ◽  
Symmetric System ◽  
Positive Real ◽  
State Matrix ◽  
Numerical Design ◽  
Positive Realness ◽  
Necessary And Sufficient ◽  
Sufficient Test ◽  
Symmetric Systems

In this article, the state-space symmetric systems with symmetrical interval uncertainty that have positive real and negative imaginary properties are studied. First, a necessary and sufficient test in view of a state matrix is derived for a state-space symmetric system to be negative imaginary, which allows having poles at the origin. Second, bounds on symmetrical interval uncertainty that guarantee the positive realness and negative imaginariness of state-space symmetric systems are provided. Finally, the main results are illustrated by a resistor–capacitor network and a numerical design example.

Robust Controllability of Interval Fractional Order Linear Time Invariant Systems

2005 ◽  
Author(s):  
Yang Quan Chen ◽  
Hyo-Sung Ahn ◽  
Dingyu¨ Xue
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Linear Time ◽  
Interval Uncertainty ◽  
State Matrix ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Robust Controllability ◽  
Time Invariant

We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in state-space form. We re-visited the controllability problem for the case when there is no interval uncertainty. It turns out that the stability check for FO-LTI systems amounts to checking the conventional integer order state space using the same state matrix A and the input coupling matrix B. Based on this fact, we further show that, for interval FO-LTI systems, the key is to check the linear dependency of a set of interval vectors. Illustrative examples are presented.

On positive realness, negative imaginariness, and H∞ control of state-space symmetric systems

Automatica ◽  
2019 ◽  
Vol 101 ◽  
pp. 190-196 ◽  
Author(s):  
Mei Liu ◽  
James Lam ◽  
Bohao Zhu ◽  
Ka-Wai Kwok
Keyword(s):  
State Space ◽  
Positive Realness ◽  
Symmetric Systems

Model reduction for state-space symmetric systems

1998 ◽  
Vol 34 (4) ◽  
pp. 209-215 ◽  
Author(s):  
W.Q. Liu ◽  
V. Sreeram ◽  
K.L. Teo
Keyword(s):  
Model Reduction ◽  
State Space ◽  
Symmetric Systems

scholarly journals An Exactly Solved Model for Mutation, Recombination and Selection

2003 ◽  
Vol 55 (1) ◽  
pp. 3-41 ◽  
Author(s):  
Michael Baake ◽  
Ellen Baake
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Sufficient Criterion ◽  
Linkage Disequilibria ◽  
Additive Type ◽  
Mean Fitness ◽  
The Mean ◽  
Necessary And Sufficient ◽  
Independent Mutation ◽  
Selection Of

AbstractIt is well known that rather generalmutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state space one started from.Here, we present a relevant subclass of such models, in continuous time, with independent mutation events at the sites, and crossover events between them. It admits a closed solution of the corresponding differential equation on the basis of the original state space, and also closed expressions for the linkage disequilibria, derived by means of Möbius inversion. As an extra benefit, the approach can be extended to a model with selection of additive type across sites. We also derive a necessary and sufficient criterion for the mean fitness to be a Lyapunov function and determine the asymptotic behaviour of the solutions.

Reversibility of Markov chains with applications to storage models

1985 ◽  
Vol 22 (01) ◽  
pp. 123-137 ◽  
Author(s):  
Hideo Ōsawa
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Risk Model ◽  
Sufficient Conditions ◽  
Single Server ◽  
General State ◽  
Insurance Risk ◽  
General State Space ◽  
Necessary And Sufficient

This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

Reversibility of Markov chains with applications to storage models

1985 ◽  
Vol 22 (1) ◽  
pp. 123-137 ◽  
Author(s):  
Hideo Ōsawa
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Risk Model ◽  
Sufficient Conditions ◽  
Single Server ◽  
General State ◽  
Insurance Risk ◽  
General State Space ◽  
Necessary And Sufficient

This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

On the rate of convergence of probabilities of moderate deviations

1970 ◽  
Vol 11 (1) ◽  
pp. 91-94 ◽  
Author(s):  
V. K. Rohatgi
Keyword(s):  
Sufficient Conditions ◽  
Moderate Deviations ◽  
Independent Random Variables ◽  
Standard Normal Distribution ◽  
Positive Real ◽  
Moment Conditions ◽  
Standard Normal ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Asymptotic Forms

Let {Xn: n ≧ 1} be a sequence of independent random variables and write Letand let . Suppose that converges in law to the standard normal distribution (see [5, 280] for necessary and sufficient conditions). Let {xn} be a monotonic sequence of positive real numbers such that xn → ∞ as n → ∞. Then as n → ∞ for all ε > 0. [6] Rubin and Sethuraman call probabilities of the form probabilities of moderate deviations and obtain asymptotic forms for such probabilities under appropriate moment conditions.

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