Realization problem for singular positive continuous-time systems with delays

Tadeusz Kaczorek

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A realization problem for positive continuoustime systems with reduced numbers of delays

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

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A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.

Canonical forms of singular 1D and 2D linear systems

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

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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...

Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays

Tadeusz Kaczorek (2005)

International Journal of Applied Mathematics and Computer Science

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The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.

Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

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The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.

Realization problem for a class of positive continuous-time systems with delays

Tadeusz Kaczorek (2005)

International Journal of Applied Mathematics and Computer Science

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The realization problem for a class of positive, continuous-time linear SISO systems with one delay is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for the computation of positive minimal realizations is presented and illustrated by an example.

Equivalence and reduction of delay-differential systems

Mohamed Boudellioua (2007)

International Journal of Applied Mathematics and Computer Science

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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...

Externally and internally positive singular discrete-time linear systems

Tadeusz Kaczorek (2002)

International Journal of Applied Mathematics and Computer Science

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Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative),...

Realization problem for positive linear systems with time delay.

Kaczorek, Tadeusz (2005)

Mathematical Problems in Engineering

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Computation of realizations composed of dynamic and static parts of improper transfer matrices

Tadeusz Kaczorek (2007)

International Journal of Applied Mathematics and Computer Science

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The problem of computing minimal realizations of a singular system decomposed into a standard dynamical system and a static system of a given improper transfer matrix is formulated and solved. A new notion of the minimal dynamical-static realization is introduced. It is shown that there always exists a minimal dynamical-static realization of a given improper transfer matrix. A procedure for the computation of a minimal dynamical-static realization for a given improper transfer matrix...