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1

Hybrid state-feedback guaranteed cost control for a class of uncertain linear delay system

Zhao C., Wang R., Zhao J.

Systems Science

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2004

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Vol. 30, no 4

81-90

EN

This paper focuses on the hybrid state-feedback guaranteed cost control problem for a class of uncertain linear delay system. Suppose there exist finite candidate controllers with known controller gain matrices and none of the controllers can make the system satisfy guaranteed cost control based on single-Lyapunov function method, sufficient conditions for hybrid state-feedback guaranteed cost control are given and hybrid state-feedback guaranteed control law is constructed. The simulation demonstrates the effectiveness of the method proposed in this paper.

2

On state and output stabilization of discrete delay systems

Karrakchou J., Namir A., Lahmidi F., Daafi B.

Archives of Control Sciences

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2004

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Vol. 14, no. 3/4

287-298

EN

The problem of the state and output stabilization of discrete-time delay systems on Hilbert spaces is considered. Sufficient and necessary conditions for the state stabilization are given. Analogue results for the output stabilization are presented. This work is organized in three sections. The state stabilization problem is examined in section 2. The three principle notions of stability and stabilizability (uniform, strong and weak) are investigated. Using the state space technique, it is shown that this problem can be tackled considering an equivalent non delayed system. Sufficient and necessary conditions for the stabilization of the new system are then established. Using these results and similar methods, sufficient and necessary conditions for the output stabilization are developed in section 3. To illustrate this work, some examples are given.

3

On the Constrained Controllability of Dynamical Systems With Multiple Delays in the State

Sikora B.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 4

469-479

EN

Linear stationary dynamical systems with multiple constant delays in the state are studied. Their relative and approximate controllability properties with constrained controls are discussed. Definitions of various types of controllability with constrained controls for systems with delays in the state are introduced. Some theorems concerning the relative and the approximate relative controllability with constrained controls for dynamical systems with delays in the state are established. Various types of constraints are considered. Numerical examples illustrate the theoretical analysis. An example of a real technical dynamical system is given to indicate one of possible practical applications of the theoretical results.

4

On controllability and minimum energy control of linear positive systems with delays

Sikora B.

Archives of Control Sciences

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2003

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Vol. 13, no. 4

431-444

EN

The positive stationary dynamical systems with multiple delays in control are considered in the paper. the definition of the relative controllability for positive systems with delays and the criterions of their relative controllability are given. The minimum energy control problem for these systems is formulated and solved. Numerical examples illustrate the theoretical analysis. The example of real, technological positive dynamical system as a practical application of the theoretical results is presented.

5

Motion Planning, Equivalence, Infinite Dimensional Systems

Rouchon P.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

165-188

EN

Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al., 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems on Monge equations and equivalence investigated by Hilbert and Cartan. The study of several examples (the car with n-trailers and the non-holonomic snake, pendulums in series and the heavy chain, the heat equation and the Euler-Bernoulli flexible beam) indicates that the notion of flatness and its underlying explicit description can be extended to infinite-dimensional systems. As in the finite-dimensional case, this property yields simple motion planning algorithms via operators of compact support. For the non-holonomic snake, such operators involve non-linear delays. For the heavy chain, they are defined via distributed delays. For heat and Euler-Bernoulli systems, their supports are reduced to a point and their definition domain coincides with the set of Gevrey functions of order 2.

6

Discrete-averaged mathematical models of neutral delay systems

Kozera W.

Archives of Control Sciences

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1998

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Vol. 7, no. 1/2

105-120

EN

This article presents a method of determining discrete-averaged mathematical models of multi-input multi-output (MIMO) linear time-invariant systems with constant commensurate delays characterized by a finite-dimensional subspace of antistable states. The proposed method generalizes the, presented in works [10 - 13], methods of determining models for retarded-delay systems to include systems of neutral type. The finite-dimensional approximation substantially facilitates analysis and enables designing the physically implemented control laws of the systems in question. To illustrate these problems, included are simple examples of determining unstable eigenvalues and of stabilization of the plant with a digital-analog (hybrid) compensator.