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1
Content available remote Zeros in linear systems with time delay in state
Tokarzewski J.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 4
609-617
EN
The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and zero dynamics. General formulas for output-zeroing inputs and zero dynamics are provided.
2
Content available remote Modelling and Validation of Secure Connection Establishment in a Generic Access Network Scenario
Kristensen L.M., Fleischer P.
Fundamenta Informaticae
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2009
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Vol. 94, nr 3/4
361-386
EN
The Generic Access Network (GAN) architecture is defined by the 3rd Generation Partnership Project (3GPP) and allows telephone services, such as SMS and voice-calls, to be accessed via Internet Protocol (IP) networks. The main usage of this is to allow mobile phones to use WiFi in addition to the usual GSM network. The GAN specification relies on the Internet Protocol Security layer (IPSec) and the Internet Key Exchange protocol (IKEv2) to provide encryption across IP networks, and thus avoid compromising the security of the telephone networks. The detailed usage of these two Internet protocols (IPSec and IKEv2) is not fully described in the GAN specification. As part of the process to develop solutions to support the GAN architecture, TietoEnator Denmark has developed a detailed GAN scenario which describes how IPSec and IKEv2 are to be used during the connection establishment procedure. This paper presents an industrial project where Coloured Petri Nets (CPNs) were used to specify and validate the detailed GAN scenario considered by TietoEnator.
3
Content available remote Zeros and the output-zeroing problem in linear systems with time delay in control vector
Tokarzewski J.
Archives of Control Sciences
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2009
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Vol. 19, no. 1
23-41
EN
The notion of zeros in linear time-invariant multi input multi output systems with delay in state or/and control input is not extensively discussed in the relevant literature. The concept of invariant zeros in a linear time-invariant MIMO system with delay in control vector is considered. In the state-space framework the invariant zeros are treated as the triples: complex number, nonzero state-zero direction, input-zero direction. Such treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is also addressed. For systems of uniform rank the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and the zero dynamics. General formulas for output-zeroing inputs, the corresponding solutions and the zero dynamics are provided. The obtained results are illustrated by simple numerical examples.
4
Content available remote A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy
Tokarzewski J.
International Journal of Applied Mathematics and Computer Science
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2004
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Vol. 14, no 2
149-159
EN
The question how the classical definition of the Smith zeros of an 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 a nonzero state-zero direction. Such a definition allows an infinite number of zeros (then the system is called degenerate). A sufficient and necessary condition for nondegeneracy is formulated. Moreover, some characterization of invariant zeros, based on the Weierstrass-Kronecker canonical form of the system and the first nonzero Markov parameter, is obtained.
5
Content available remote Relationship between Smith zeros and invariant zeros in linear systems
Tokarzewski J.
Archives of Control Sciences
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2004
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Vol. 14, no. 1
15-26
EN
The question how the classical concept of the Smith zeros of a linear, time-invariant (LTI), multi-input, multi-output (MIMO) continuous-time singular system S (E, A, B, C, D) can be generalized and related to the stste-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 aforementioned generalization treats zeros (called further the invariant zeros) as the triples . Such treatment is strictly connested with the output-zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case.
6
Feedback control for discrete descriptor systems
Kurina G.A.
Systems Science
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2002
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Vol. 28, nr 2
29-40
EN
The control in the feedback form and the optimal cost are obtained for four linear-quadratic control problems by discrete descriptor systems in a Hilbert space. Special solutions of the implicit operator Riccati equations used here act in all state space and in general case they are not nonnegative definite, unlike the operators in the subspace and the nonnegative definite solutions. The examples show that the operator Riccati equations considered have no nonnegative definite solutions though the corresponding optimal control problems have the unique solutions.
7
Content available remote A general solution to the output-zeroing problem for MIMO LTI systems
Tokarzewski J.
International Journal of Applied Mathematics and Computer Science
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2002
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Vol. 12, no 2
161-171
EN
The problem of zeroing the output in an arbitrary linear continuous-time system S(A,B,C,D) with a nonvanishing transfer function is discussed and necessary conditions for output-zeroing inputs are formulated. All possible real-valued inputs and real initial conditions which produce the identically zero system response are characterized. Strictly proper and proper systems are discussed separately.
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