1 Positive Linear Switched Systems Are Not Uniformly Asymptotically Stable, Even For n = 3 (2009)
Lior Fainshil, Michael Margaliot, Pavel Chigansky
We consider n-dimensional positive linear switched systems. A necessary condition for stability under arbitrary switching is that every matrix in the convex hull of the matrices defining the...
MATHEMATICAL MODELING OF THE λ SWITCH-- A FUZZY LOGIC APPROACH (2009)
Dmitriy Laschov, Michael Margaliot
Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important...
STABILITY ANALYSIS OF SECOND-ORDER SWITCHED HOMOGENEOUS SYSTEMS ∗ (2009)
David Holcman, Michael Margaliot
Abstract. We study the stability of second-order switched homogeneous systems. Using the concept of generalized first integrals we explicitly characterize the “most destabilizing ” switching-law...
Analysis of a Flying Capacitor Converter: A Switched Systems Approach (2009)
Alex Ruderman, Boris Reznikov, Michael Margaliot
Flying capacitor converters (FCCs) attract considerable interest because of their inherent natural voltage balancing property. Several researchers analyzed the voltage balance dynamics in FCCs using...
Analysis of Learning Near Temporary Minima Using the All Permutations Fuzzy Rule-Base (2009)
Abstract—An important problem in learning using gradient descent algorithms (such as backprop) is the slowdown incurred by temporary minima (TM). We consider this problem for a network trained to...
Michael Margaliot, Michael S. Branicky
We consider planar bilinear control systems with measurable controls. We show that any point in the reachable set can be reached by a “nice ” control. Specifically, a control that is a...
Abstract Design and Analysis of Fuzzy Schedulers using Fuzzy Lyapunov Synthesis (2008)
Michael Margaliot, Gideon Langholz
Recently, the authors suggested a new approach to the design offuzzy control rules. The method, re-ferred to as fuzzy Lyapunov synthesis, extends clas-sical Lyapunov synthesis to the domain of...
A Simplification of the Agrachev-Gamkrelidze Second-Order Maximum Principle (2008)
Irad Ratmansky, Michael Margaliot
The Agrachev-Gamkrelidze maximum principle (AGMP) provides a necessary second-order condition for the optimality of bang-bang controls, which is stronger than the condition provided by the...
A Lie-Algebraic Analysis of the Problem of Absolute Stability ∗ (2008)
Michael Margaliot, Christos Yfoulis
The absolute stability problem (ASP) entails determining a critical parameter value for which the stability of a feedback system, composed of an nth-order linear system and a sector-bounded nonlinear...
Michael Margaliot, Michael S. Branicky
We derive a new reachability with nice controls type result for planar bilinear control systems. We show that any point in the reachable set can be reached by a control that is a concatenation of a...
Third-Order Nilpotency, Nice Reachability (2008)
And Asymptotic Stability, Yoav Sharon, Michael Margaliot
We consider an a#ne control system whose vector fields span a third-order nilpotent Lie algebra. We show that the reachable set at time T using measurable controls is equivalent to the reachable set...
Submitted to Systems and Control Letters 1 Lie-algebraic stability conditions for nonlinear (2008)
Switched Systems And, Michael Margaliot, Daniel Liberzon
We present a stability criterion for switched nonlinear systems which involves Lie brackets of the individual vector fields but does not require that these vector fields commute. A special case of...
A Counter Example to a Conjecture of Gurvits (2008)
On Switched Systems, Michael Margaliot
We consider products of matrix exponentials under the assumption that the matrices span a nilpotent Lie algebra. In 1995, Leonid Gurvits conjectured that nilpotency implies that these products are,...
We consider the problem of absolute stability of a feedback system composed of a linear plant and a single sector-bounded nonlinearity. Pyatnitskiy and Rapoport used a variational approach and the...
How Does the Dendrocoleum lacteum Orient to Light? A Fuzzy Modeling Approach (2007)
Eviatar Tron, Michael Margaliot
We apply fuzzy modeling to derive a mathematical model for a biological phenomena: the orientation to light of the planarian Dendrocoleum lacteum. This behavior was described linguistically by...
Hyperbolic Approach to Fuzzy Control Is Optimal Hung T. Nguyen 1 (2007)
Vladik Kreinovich, Michael Margaliot, Gideon Langholtz
(contact author)
Many Practical Control Situations Can Be Adequately (2007)
Hung T. Nguyen, Vladik Kreinovich, Michael Margaliot, Gideon Langholtz
Abstract---In a series of papers and a book, M. Margaliot and G. Langholz proposed a hyperbolic approach to fuzzy control, in which they apply a certain hyperbolic non-linear transformation to the...
Michael Margaliot, Gideon Langholz
The rotational/translational proof-mass actuator (RTAC) system is a well-known benchmark for nonlinear control for which a number of controllers were designed. In this paper we apply fuzzy Lyapunov...
Stability Analysis of Second-Order Switched Homogeneous Systems (2007)
David Holcman, Michael Margaliot
We study the stability of second-order switched homogeneous systems. Using the concept of generalized first integrals we explicitly characterize the "most destabilizing" switching-law and...
A New Approach to Fuzzy Modeling and Control of Discrete-Time Systems (2007)
Michael Margaliot, Gideon Langholz
We present a new approach to fuzzy modeling and control of discrete-time systems which is based on the formulation of a novel state-space representation using the hyperbolic tangent function. The new...
On the Reachable Set of Nonlinear Control (2007)
Systems With Nilpotent, Michael Margaliot
We consider control systems that are affine in the control and whose vector fields generate a nilpotent Lie algebra. Analysis of such systems can be reduced to the analysis of the associated...
Nicholson's Blowflies Revisited: (2007)
Fuzzy Modeling Approach, Iosef Rashkovsky, Michael Margaliot
We apply fuzzy modeling to derive a mathematical model for a biological phenomenon: the regulation of population size in the Australian sheep-blowfly Lucilia cuprina. This behavior was described by...
Valeri Rozin And, Valeri Rozin, Michael Margaliot
The design of artificial systems inspired by biological behavior is recently attracting considerable interest. Many biological agents such as plants or animals were forced to develop sophisticated...
Biomimicry and Fuzzy Modeling: A Match Made in Heaven (2007)
Biomimicry, the design of artificial systems that mimic natural behavior, is recently attracting considerable interest. Biomimicry requires a reverse engineering process; the behavior of a biological...
Mathematical modeling of natural phenomena: a fuzzy logic approach (2007)
Summary. In many fields of science human observers have provided verbal descriptions and explanations of various systems. A formal mathematical model is indispensable when we wish to rigorously...
A New Approach to Knowledge-Based Design of Recurrent Neural Networks (2006)
Eyal Kolman, Michael Margaliot
We develop a new approach for designing a recurrent neural network (RNN) that is suitable for solving a given problem. Initial information on the problem domain is stated in terms of symbolic If-Then...
Extracting Symbolic Knowledge from Recurrent Neural Networks - A Fuzzy Logic Approach (2006)
Eyal Kolman, Michael Margaliot
Considerable research has been devoted to the integration of fuzzy logic (FL) tools with classic artificial intelligence (AI) paradigms. One reason for this is that FL provides powerful mechanisms...
Knowledge Extraction from Neural Networks Using the All-Permutations Fuzzy Rule Base (2005)
Eyal Kolman, Michael Margaliot
A major drawback of artificial neural networks is their black-box character. Even when the trained network performs adequately, it is very di#cult to understand its operation. In this paper, we use...
Mathematical modeling of observed natural behavior: a fuzzy logic approach (2004)
Eviatar Tron, Michael Margaliot
Fuzzy modeling is routinely used to transform the knowledge of an expert, be it a physician or a process operator, into a mathematical model. The emphasis is on constructing a fuzzy expert system...
Are Artificial Neural Networks White Boxes? (2004)
Eyal Kolman, Michael Margaliot
We introduce a novel Mamdani-type fuzzy model, referred to as the all-permutations fuzzy rule-base, and show that it is mathematically equivalent to a standard feedforward neural network. We describe...
Mathematical modeling of observed natural behavior: a fuzzy logic approach (2004)
Eviatar Tron, Michael Margaliot
fuzzy logic approach
Root-mean-square gains of switched linear systems (2003)
Michael Margaliot, João P. Hespanha
Abstract — We consider the problem of computing the rootmean-square (RMS) gain of switched linear systems. We develop a new approach which is based on an attempt to characterize the “worst-case...
Switching in Systems and (2003)
Michael Margaliot, Daniel Liberzon
Lie-algebraic stability conditions for nonlinear
Some nonlinear optimal control problems with closed-form solutions (2001)
Michael Margaliot, Gideon Langholz
Optimal controllers guarantee many desirable properties including stability and robustness of the closed-loop system. Unfortunately, the design of optimal controllers is generally very dicult because...
The Routh-Hurwitz Array and Realization of Characteristic Polynomials (2000)
Michael Margaliot, Gideon Langholz
In this paper we show that the Routh-Hurwitz array of a given characteristic polynomial provides all the information required to realize the polynomial using an electrical circuit. This new...
Hyperbolic optimal control and fuzzy control (1999)
Michael Margaliot, Gideon Langholz
In this paper we consider a new approach to fuzzy control which entails the formulation of a novel state-space representation and a new form of optimal control problem. Basically, in this new...
Fuzzy Lyapunov Based Approach to the Design of Fuzzy Controllers (1999)
Michael Margaliot, Gideon Langholz
In this paper we extend the classical Lyapunov synthesis method to the design of fuzzy controllers. Assuming minimal knowledge about the plant to be controlled, the proposed method enables us to...
Necessary and sufficient conditions for absolute stability: the case of second-order systems (1997)
Michael Margaliot, Gideon Langholz
Absolute stability is perhaps the most well-known open problem in control theory as easily verifiable necessary and sufficient conditions for absolute stability have remained unattainable since the...