2017 (vol. 27) - Number 2

*W. Bozejko, M. Wodecki:*

Discrete Systems: Theory and Applications. Special issue.

*G. Bocewicz, Z. Banaszak, I. Nielsen:*

Delivery-flow routing and scheduling subject to constraints imposed by vehicle flows in fractal-like networks

*W. Bozejko, A. Gnatowski, R. Idzikowski, M. Wodecki:*

Cyclic flow shop scheduling problem with two-machine cells

*W. Bozejko, M. Uchronski,, Z. Chaczko, M. Wodecki:*

Parallel patterns determination in solving cyclic flow shop problem with setups

*J. Brodny, S. Alszer, J. Krystek, M. Tutak:*

Availability analysis of selected mining machinery

*K. Chmielewska, D. Formanowicz, P. Formanowicz:*

The effect of cigarette smoking on endothelial damage and atherosclerosis development - modeled and analyzed using Petri nets

*A. Galuszka, J. Krystek, A. Swierniak, T. Grzejszczak, C. Lungoci:*

Information management in passenger traffic supporting system design as a multi-criteria discrete optimization task

*M. Kardynska, J. Smieja:*

Sensitivity analysis of signaling pathway models based on discrete-time measurements

*J. Kasprzyk, P. Krauze, S. Budzan, J. Rzepecki:*

Vibration control in semi-active suspension of the experimental off-road vehicle using information about suspension deflection

*M. Koryl, D. Mazur:*

Towards emergence phenomenon in business process management

*M. Koryl:*

Active resources concept of computation for enterprise software

*H. Krawczyk, M. Nykiel:*

Mobile devices and computing cloud resources allocation for interactive applications

*W. Mitkowski, W. Bauer, M. Zagórowska:*

Discrete-time feedback stabilization

*J. Pempera:*

An exact block algorithm for no-idle RPQ problem

*K. Rzosinska, D. Formanowicz, P. Formanowicz:*

The study of the influence of micro-environmental signals on macrophage differentiation using a quantitative Petri net based model

*K. Skrzypczyk , M. Mellado:*

Vehicle navigation in populated areas using predictive control with environmental uncertainty handling

*W. Bozejko, J. Pempera, M. Wodecki:*

A fine-grained parallel algorithm for the cyclic flexible job shop problem

ACS Abstract:

**2004 (Volume 14)**

Number 2

**Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistance**

Marek Kimmel(Rice University, USA) | Andrzej ¦wierniak(Silesian University of Technology, Poland) |

**keywords:** optimal control, biomathematical models, cancer chemotherapy, bilinear systems, cell cycle dynamics.

**- norm computation for stable linear continuous-time periodic systems**

B.P. Lampe(University of Rostock, Germany) | M. Obraszov and E. Rosenwasser(St. Petersburg State University of Ocean Technology, Russia) |

*T*is the period of the system, and it operates only with matrices of finite dimension. An example is given, where the -norm is determined exactly, and the proposed method turns out to be superior to other known methods.

**keywords:** time-varying systems, periodic motion, Laplace transforms, Green functions, transfer functions, norms.

**A controllability problem for a class of uncertain - parameters discrete-time linear dynamic systems**

Krzysztof Oprzedkiewicz(University of Mining and Metallurgy, Poland) |

**keywords:** linear discrete-time systems with uncertain parameters, controllability.

**A note on zeros, output-nulling subspaces and zero-dynamics in MIMO LTI systems**

Jerzy Tokarzewski(Military University of Technology, Poland) |

*S(A,B,C)*the classical notion of the Smith zeros does not characterize fully the output-zeroing problem nor the zero dynamics. The question how this notion can be extended and related to the state-space methods is discussed. Nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The proposed extension treats multivariable zeros (called further the invariant zeros) as the triples (complex number, nonzero state-zero direction, input-zero direction). Such a treatment is strictly connected with the output zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case (i.e., when any complex number is such a zero).

A simple sufficient and necessary condition of nondegeneracy is presented. The condition decomposes the class of all systems

*S(A,B,C)*such that

*B*

*0*and

*C*

*0*into two disjoint subclasses: of nondegenerate and degenerate systems. In nondegenerate systems the Smith zeros and the invariant zeros are exactly the same objects which are determined as the roots of the so-called zero polynomial. The degree of this polynomial equals the dimension of the maximal

*(A,B)*-invariant subspace contained in ker

*C*, while the zero dynamics are independent upon control vector. In degenerate systems the zero polynomial determines merely the Smith zeros, while the set of the invariant zeros equals the whole complex plane. The dimension of the maximal

*(A,B)*-invariant subspace contained in ker

*C*is strictly larger than the degree of the zero polynomial, whereas the zero dynamics essentially depend upon control vector.

**keywords:** linear systems, zeros, degeneracy, zero dynamics, Markov parameters, singular value decomposition.

**A time-varying switching plane design for variable structure control of the third order system with input constraint**

Andrzej Bartoszewicz and Aleksandra Nowacka(Technical University of £ód¼, Poland) |

**keywords:** sliding mode control, variable structure systems, time-varying switching planes, switching surface design.

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