Discrete Nonstationary Bounded Real Lemma in Indefinite Metrics, the Strict Contractive Case

1995 ◽  
pp. 49-78 ◽  
Author(s):  
A. Ben-Artzi ◽  
I. Gohberg ◽  
M. A. Kaashoek
Keyword(s):  
Bounded Real Lemma ◽  
Indefinite Metrics

Robust H2/H∞Control Strategy for Linear Markovian Jump Systems

2014 ◽  
Vol 525 ◽  
pp. 646-652
Author(s):  
Min Bian ◽  
Qing Yun Guo
Keyword(s):  
Control Strategy ◽  
State Feedback ◽  
Control Strategies ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Bounded Real Lemma ◽  
Finite State ◽  
Linear State ◽  
Feasible Solutions ◽  
Jump Systems

The robust H2/<em>H</em>∞ control strategy for a class of linear continuous-time uncertain systems with randomly jumping parameters is investigated. The transition of the jumping parameters is decided by a finite-state Markov process. The uncertainties are supposed to be norm-bounded. It is desired to design a linear state feedback control strategies such that the closed-loop system satisfies H performance and minimizes the H2 norm of the system. A sufficient condition is first established on the existence of the robust H2/<em>H</em>∞controller bases on the bounded real lemma. Then the corresponding state-feedback law is given in terms of a set of linear matrix inequalities (LMIs). It is showed that this condition is equivalent to the feasible solutions problem of LMI. Furthermore, the control strategy design problem is converted into a convex optimization problem subject to LMI constraints, which can be easily solved by standard numerical software.

Monotonically convergent ILC systems designed using bounded real lemma

2012 ◽  
Vol 43 (11) ◽  
pp. 2062-2071 ◽  
Author(s):  
Deyuan Meng ◽  
Yingmin Jia ◽  
Junping Du ◽  
Fashan Yu
Keyword(s):  
Bounded Real Lemma

scholarly journals Singular finite-gap operators and indefinite metrics

2009 ◽  
Vol 64 (4) ◽  
pp. 625-650 ◽  
Author(s):  
Petr G Grinevich ◽  
Sergei P Novikov
Keyword(s):  
Indefinite Metrics

Order Reduction of Controller Based on LMIs Improving Error Bounds

1997 ◽  
Author(s):  
Roberd Saragih ◽  
Yoshida Kazuo
Keyword(s):  
Projection Method ◽  
Order Reduction ◽  
Feasibility Problem ◽  
Closed Loop System ◽  
Reduced Order ◽  
Bounded Real Lemma ◽  
Convex Feasibility ◽  
Alternating Projection ◽  
Alternating Projection Method ◽  
Order Reduction Method

Abstract In this paper, we propose an order reduction method of controller based on combination of the alternating projection method and the balanced truncation. In this method both the errors of controller and the closed-loop system caused by the reduced-order controller can be improved simultaneously. By using a generalized Bounded Real Lemma, a feasible reduced-order controller can be derived. The sufficient condition for the existence of a reduced-order controller leads to a non-convex feasibility problem. To solve the problem, we can use an improved computational scheme based on the alternating projection method. But it is needed so much time to solve the problem if compared by the other methods. To validate the proposed method, some numerical calculations and simulations are carried out.

4-VECTOR FIELDS AND INDEFINITE METRICS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1317-1332 ◽  
Author(s):  
VALERI V. DVOEGLAZOV
Keyword(s):  
Lorentz Group ◽  
Vector Fields ◽  
Mass Generation ◽  
Indefinite Metrics ◽  
Modern Physics ◽  
Stueckelberg Formalism

We generalize the Stueckelberg formalism in the (1/2, 1/2) representation of the Lorentz Group, see Ref. 1–2. We analize the problem of the mass generation and of the indefinite metrics from the modern viewpoints, see Ref. 3–4. Some relations to other modern-physics models are found.

scholarly journals H2/H∞ Control for MJLS with Infinite Markov Chain

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Ting Hou ◽  
Jie Wang ◽  
Yueying Liu ◽  
Xiao Shen
Keyword(s):  
Markov Chain ◽  
Control Problem ◽  
Discrete Time ◽  
Control Design ◽  
Finite Horizon ◽  
Bounded Real Lemma ◽  
Infinite Set

With the help of a stochastic bounded real lemma, we deal with finite horizon H2/H∞ control problem for discrete-time MJLS, whose Markov chain takes values in an infinite set. Besides, a unified control design for H2, H∞, and H2/H∞ is given.

Improved delay-dependent bounded real lemma for uncertain time-delay systems

2009 ◽  
Vol 179 (20) ◽  
pp. 3711-3719 ◽  
Author(s):  
Tao Li ◽  
Lei Guo ◽  
Xin Xin
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Bounded Real Lemma ◽  
Uncertain Time ◽  
Delay Dependent
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