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Parametric control to quasi-linear systems based on dynamic compensator and multi-objective optimization

Da-Ke Gu, Da-Wei Zhang (2020)

Kybernetika

This paper considers a parametric approach for quasi-linear systems by using dynamic compensator and multi-objective optimization. Based on the solutions of generalized Sylvester equations, we establish the more general parametric forms of dynamic compensator and the left and right closed-loop eigenvector matrices, and give two groups of arbitrary parameters. By using the parametric approach, the closed-loop system is converted into a linear constant one with a desired eigenstructure. Meanwhile,...

Parametrization and reliable extraction of proper compensators

Ferdinand Kraffer, Petr Zagalak (2002)

Kybernetika

The polynomial matrix equation X l D r + Y l N r = D k is solved for those X l and Y l that give proper transfer functions X l - 1 Y l characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly...

Partial disturbance decoupling problem for structured transfer matrix systems by measurement feedback

Ulviye Başer (1999)

Kybernetika

Partial disturbance decoupling problems are equivalent to zeroing the first, say k Markov parameters of the closed-loop system between the disturbance and controlled output. One might consider this problem when it is not possible to zero all the Markov parameters which is known as exact disturbance decoupling. Structured transfer matrix systems are linear systems given by transfer matrices of which the infinite zero order of each nonzero entry is known, while the associated infinite gains are unknown...

Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control

Y. Kanevsky, A.A. Nepomnyashchy (2010)

Mathematical Modelling of Natural Phenomena

A global feedback control of a system that exhibits a subcritical monotonic instability at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero mode. The method based on a variational principle is applied for the derivation of a low-dimensional evolution model. In the framework of this model the investigation of the system’s dynamics...

Polynomial controller design based on flatness

Frédéric Rotella, Francisco Javier Carillo, Mounir Ayadi (2002)

Kybernetika

By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.

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.

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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