Displaying similar documents to “Reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems”

Positive 2D discrete-time linear Lyapunov systems

Przemysław Przyborowski, Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

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Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Alexey Zhirabok, Alexey Shumsky (2012)

International Journal of Applied Mathematics and Computer Science

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The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems,...

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.

Controllability in the max-algebra

Jean-Michel Prou, Edouard Wagneur (1999)

Kybernetika

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We are interested here in the reachability and controllability problems for DEDS in the max-algebra. Contrary to the situation in linear systems theory, where controllability (resp observability) refers to a (linear) subspace, these properties are essentially discrete in the max -linear dynamic system. We show that these problems, which consist in solving a max -linear equation lead to an eigenvector problem in the min -algebra. More precisely, we show that, given a max -linear system, then, for...

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.

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...