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Polynomial systems theory applied to the analysis and design of multidimensional systems

Jari Hatonen, Raimo Ylinen (2003)

International Journal of Applied Mathematics and Computer Science

The use of a principal ideal domain structure for the analysis and design of multidimensional systems is discussed. As a first step it is shown that a lattice structure can be introduced for IO-relations generated by polynomial matrices in a signal space X (an Abelian group). It is assumed that the matrices take values in a polynomial ring F[p] where F is a field such that F[p] is a commutative subring of the ring of endomorphisms of X. After that it is analysed when a given F[p] acting on X can...

Positive 2D discrete-time linear Lyapunov systems

Przemysław Przyborowski, Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

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.

Positive stable realizations of fractional continuous-time linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.

Positivity and stabilization of 2D linear systems

Tadeusz Kaczorek (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.

Powerful nonlinear observer associated with field-oriented control of an induction motor

Abdellah Mansouri, Mohammed Chenafa, Abderrahmane Bouhenna, Eric Etien (2004)

International Journal of Applied Mathematics and Computer Science

In this paper, we associate field-oriented control with a powerful nonlinear robust flux observer for an induction motor to show the improvement made by this observer compared with the open-loop and classical estimator used in this type of control. We implement this design strategy through an extension of a special class of nonlinear multivariable systems satisfying some regularity assumptions. We show by an extensive study that this observer is completely satisfactory at low and nominal speeds...

Predictability and control synthesis

Philippe Declerck (1999)

Kybernetika

Processes modeled by a timed event graph may be represented by a linear model in dioïd algebra. The aim of this paper is to make temporal control synthesis when state vector is unknown. This information loss is compensated by the use of a simple model, the “ARMA” equations, which enables to introduce the concept of predictability. The comparison of the predictable output trajectory with the desired output determines the reachability of the objective.

Predictive control for trajectory tracking and decentralized navigation of multi-agent formations

Ionela Prodan, Sorin Olaru, Cristina Stoica, Silviu-Iulian Niculescu (2013)

International Journal of Applied Mathematics and Computer Science

This paper addresses a predictive control strategy for a particular class of multi-agent formations with a time-varying topology. The goal is to guarantee tracking capabilities with respect to a reference trajectory which is pre-specified for an agent designed as the leader. Then, the remaining agents, designed as followers, track the position and orientation of the leader. In real-time, a predictive control strategy enhanced with the potential field methodology is used in order to derive a feedback...

Proper feedback compensators for a strictly proper plant by polynomial equations

Frank Callier, Ferdinand Kraffer (2005)

International Journal of Applied Mathematics and Computer Science

We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...

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