2022 (vol. 32) - Number 1

*J. Cvejn:*

The magnitude optimum design of the PI controller for plants with complex roots and dead time

*S.F. Al-Azzawi, M.A. Hayali:*

Coexisting of self-excited and hidden attractors in a new 4D hyperchaotic Sprott-S system with a single equilibrium point

*M.A. Hammami, N. El Houda Rettab, F. Delmotte:*

On the state estimation for nonlinear continuous-time fuzzy systems

*M. Ilyas, M.A. Khan, A. Khan, Wei Xie, Y. Khan:*

Observer design estimating the propofol concentration in PKPD model with feedback control of anesthesia administration

*L. Moysis, M. Tripathi, M. Marwan:*

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

*S. Vaidyanathan, K. Benkouider, A. Sambas:*

A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation

*T.T. Tuan, H. Zabiri, M.I.A. Mutalib, Dai-Viet N. Vo:*

Disturbance-Kalman state for linear offset free MPC

*Yuan Xu, Jun Wang:*

A novel multiple attribute decision-making method based on Schweizer-Sklar *t*-norm and *t*-conorm with *q*-rung dual hesitant fuzzy information

*T. Kaczorek:*

Observers of fractional linear continuous-time systems

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) |

Two major obstacles against successful chemotherapy of cancer are the cell-cycle-phase dependence of treatment, and the emergence of resistance of cancer cells to cytotoxic agents. One way to understand and overcome these two problems is to apply optimal control theory to mathematical models of cell cycle dynamics. These models should include division of the cell cycle into subphases and/or the mechanisms of drug resistance. We review our relevant results in mathematical modelling and control of the cell cycle and of the mechanisms of gene amplification (related to drug resistance), and estimation of parameters of the constructed models.

**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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