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5 Systems Science

5 2003

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On the reconstruction of the current state of the linear difference-differential system with commensurable delays

Khartouski V.

Systems Science

2003

Vol. 29, nr 4

55-67

In the present paper, we consider the problem of reconstruction of the current state of the difference-differential system with commensurable delays. The results obtained are used for the reconstruction of the current states of linear retarded partial parabolic differential equation.

Invariant zeros in singular systems - Algebraic criterions of nondegeneracy

Tokarzewski J.

Systems Science

2003

Vol. 29, nr 1

61-78

The question of how the classical concept of the Smith zeros of a LTI continuous-time singular control system S(E,A,B,C,D) can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with nonzero state-zero direction. Such a definition admits an infinite number of zeros (then the system is called degenerate). Algebraic criterions of degeneracy/nondegeneracy based on Weierstrass-Kronecker canonical form of the system and on the first nonzero Markov parameter are analyzed.

Feedback and pole assignment of the second order singular distributed parameter control systems

Ge Z., Zhang B.

Systems Science

2003

Vol. 29, nr 4

19-27

Pole assignment for infinite many poles of the second order singular distributed parameter control system was discussed via functional analysis and operator theory in Hubert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This research is theoretically important for studying the stabilization and asymptotic stability of the second order singular distributed parameter control system.

Computation of minimal realizations for compartmental linear systems

Kaczorek T.

Systems Science

2003

Vol. 29, nr 1

15-29

A new method for computation of minimal compartmental realizations of a proper transfer function is proposed. The method is based on a suitable transformation of an asymptotically stable positive realization to the desired compartmental realization. The transformation is characterized by a generalized permutation matrix. Sufficient conditions for the existence of minimal compartmental realizations are established. Two-step procedures for computation of minimal compartmental realizations for both continuous-time and discrete-time linear systems are derived and illustrated by a numerical example.

Adaptive sliding mode backstepping output tracking controllers for feedforward uncertain systems

Koshkouei A.J., Burnham K.J.

Systems Science

2003

Vol. 29, nr 1

79-96

Methods for control design for nonlinear feedforward uncertain systems are considered in this paper. These systems are not usually transformable to the parametric semi-strict feedback form, and it may include unmatched uncertainties consisting of disturbances and unmodelled dynamics. The design methods are based upon (i) the backstepping approach, and (ii) a combination of sliding mode and backstepping. A comparison method of the dynamic and static backstepping methods is presented by applying two methods on a gravity-flow/pipeline system.