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H ∞ control of discrete-time linear systems constrained in state by equality constraints

Dušan Krokavec (2012)

International Journal of Applied Mathematics and Computer Science

In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task....

Hoptf bifurcation from infinity for planar control systems.

Jaume Llibre, Enrique Ponce (1997)

Publicacions Matemàtiques

Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For such systems, sufficient and necessary conditions for bifurcation of a limit cycle from the periodic orbit at infinity are given.

Independence of asymptotic stability of positive 2D linear systems with delays of their delays

Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.

Iterative estimators of parameters in linear models with partially variant coefficients

Shaolin Hu, Karl Meinke, Rushan Chen, Ouyang Huajiang (2007)

International Journal of Applied Mathematics and Computer Science

A new kind of linear model with partially variant coefficients is proposed and a series of iterative algorithms are introduced and verified. The new generalized linear model includes the ordinary linear regression model as a special case. The iterative algorithms efficiently overcome some difficulties in computation with multidimensional inputs and incessantly appending parameters. An important application is described at the end of this article, which shows that this new model is reasonable and...

ℓ 1 -optimal control for multirate systems under full state feedback

Johannes Aubrecht, Petros G. Voulgaris (1999)

Kybernetika

This paper considers the minimization of the ℓ ∞ -induced norm of the closed loop in linear multirate systems when full state information is available for feedback. A state-space approach is taken and concepts of viability theory and controlled invariance are utilized. The essential idea is to construct a set such that the state may be confined to that set and that such a confinement guarantees that the output satisfies the desired output norm conditions. Once such a set is computed, it is shown that...

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