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A differential geometric setting for dynamic equivalence and dynamic linearization

Jean-Baptiste Pomet (1995)

Banach Center Publications

This paper presents an (infinite-dimensional) geometric framework for control systems, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise: equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framework that dynamic equivalence of single-input systems is the same as static equivalence.

A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

Navdeep Goel, Kulbir Singh (2013)

International Journal of Applied Mathematics and Computer Science

The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution...

A separation principle for the stabilization of a class of time delay nonlinear systems

Amel Benabdallah (2015)


In this paper, we establish a separation principle for a class of time-delay nonlinear systems satisfying some relaxed triangular-type condition. Under delay independent conditions, we propose a nonlinear time-delay observer to estimate the system states, a state feedback controller and we prove that the observer-based controller stabilizes the system.

Algebraic condition for decomposition of large-scale linear dynamic systems

Henryk Górecki (2009)

International Journal of Applied Mathematics and Computer Science

The paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one of the symmetric functions of those polynomials of lower degrees is sufficient for factorization of the...

Balanced reduction of linear periodic systems

Sauro Longhi, Giuseppe Orlando (1999)


For linear periodic discrete-time systems the analysis of the model error introduced by a truncation on the balanced minimal realization is performed, and a bound for the infinity norm of the model error is introduced. The results represent an extension to the periodic systems of the well known results on the balanced truncation for time-invariant systems. The general case of periodically time-varying state-space dimension has been considered.

Canonical forms of singular 1D and 2D linear systems

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence...

Complementary matrices in the inclusion principle for dynamic controllers

Lubomír Bakule, José Rodellar, Josep M. Rossell (2003)


A generalized structure of complementary matrices involved in the input-state- output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary...

Continuous-time input-output decoupling for sampled-data systems

Osvaldo Maria Grasselli, Laura Menini (1999)


The problem of obtaining a continuous-time (i. e., ripple-free) input-output decoupled control system for a continuous-time linear time-invariant plant, by means of a purely discrete-time compensator, is stated and solved in the case of a unity feedback control system. Such a control system is hybrid, since the plant is continuous-time and the compensator is discrete-time. A necessary and sufficient condition for the existence of a solution of such a problem is given, which reduces the mentioned...

Control Systems on the Orthogonal Group SO(4)

Ross M. Adams, Rory Biggs, Claudiu C. Remsing (2013)

Communications in Mathematics

We classify the left-invariant control affine systems evolving on the orthogonal group S O ( 4 ) . The equivalence relation under consideration is detached feedback equivalence. Each possible number of inputs is considered; both the homogeneous and inhomogeneous systems are covered. A complete list of class representatives is identified and controllability of each representative system is determined.

Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

Mehmet Emir Koksal (2016)

Open Mathematics

Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation...

Equivalence and reduction of delay-differential systems

Mohamed Boudellioua (2007)

International Journal of Applied Mathematics and Computer Science

A new direct method is presented which reduces a given high-order representation of a control system with delays to a first-order form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann's strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural...

Equivalence of control systems with linear systems on Lie groups and homogeneous spaces

Philippe Jouan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only if the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field is obtained by adding a left invariant one. Its projection on a homogeneous space, whenever it exists,...

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