2020 (vol. 30) - Number 4

*A.B. Malinowska, R. Kamocki, R. Almeida, T. Odzijewicz:*

On the existence of optimal consensus control for the fractional Cucker--Smale model

*R. Grymin, W. Bożejko, J. Pempera, M. Wodecki, Z. Chaczko:*

Algorithm for solving the Discrete-Continuous Inspection Problem

*T. Kaczorek, A. Ruszewski:*

Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

*R. Arora, K. Gupta:*

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

*P. Nowak, J. Czeczot, P. Grelewicz:*

Tuning rules for industrial use of the second-order Reduced Active Disturbance Rejection Controller

*M.I. Gomoyunov:*

Optimal control problems with a fixed terminal time in linear fractional-order systems

*Muhafzan, A. Nazra, L. Yulianti, Zulakmal, R. Revina:*

On LQ optimization problem subject to fractional order irregular singular systems

*M. Blizorukova, V. Maksimov:*

On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

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 Świerniak(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 Łódź, Poland) |

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

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