Non-commensurate Time Delays Research Articles

Input-to-State Stability Analysis of Partial-Element Equivalent-Circuit Models

A full wave description of electromagnetic coupling occurring in circuits has to consider time delays. The retarded partial-element equivalent-circuit ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> PEEC) method is one of the approaches which allows us to take time delays resulting in a set of neutral functional differential equations into account. Due to the fragility of electromagnetic solvers, the asymptotic stability is a key issue in PEEC modeling. This paper presents an innovative method, based on linear matrix inequalities, to study the input-to-state stability of PEEC models with multiple noncommensurate time delays. Numerical results are given to illustrate the effectiveness of the proposed method.

A State Observer for a Class of Nonlinear Systems with Multiple Discrete and Distributed Time Delays

This paper considers the state observer problem for a class of nonlinear systems, which present multiple noncommensurate time delays as well as distributed delay terms. The proposed algorithm is an extension of the observer for nonlinear delayless systems proposed in 1993 by Ciccarella, Dalla Mora and Germani. It is proved that a suitable gain can be easily chosen such that the observation error goes to zero exponentially, with arbitrarily fixed decay rate.

Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays

The paper is to investigate the asymptotic stability for a general class of linear time-invariant singularly perturbed systems with multiple non-commensurate time delays. It is a common practice to investigate the asymptotic stability of the original system by establishing that of its slow subsystem and fast subsystem. A frequency-domain approach is first presented to determine a sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model), which is a singular system with multiple time delays, and the fast subsystem. Two delay-dependent criteria, ε-dependent and ε-independent, are then proposed in terms of the H∞-norm for the asymptotic stability of the original system. Furthermore, a simple estimate of an upper bound ε* of singular perturbation parameter ε is proposed so that the original system is asymptotically stable for any ε∈0,ε*. Two numerical examples are provided to illustrate the use of our main results.

Finite spectrum assignment for linear systems with non-commensurate time-delays

This paper studies finite spectrum assignment for linear scalar systems with non-commensurate time-delays based on a practically important class of finite Laplace transforms. The finite spectrum assignability can be reduced to the solvability of a Bezout equation over a multivariable polynomial ring with coefficients in the class of finite Laplace transforms. It is shown that, in the non-commensurate delay case, spectral canonicity is not sufficient for the finite spectrum assignability.

状態むだ時間非線形システムの有限極配置

In this paper single input nonlinear systems with non-commensurate time-delays in state variables are considered. The objective is to design a coordinates transformation and a feedback which yield a finite dimensional linear controllable closed-loop system in a new coordinates, whose spectrum is located at an arbitrarily preassigned set of n points in the complex plane. An algebraic design procedure for this problem is proposed here. The proposed method is related to the exact linearization technique for systems with a finite dimension, and recognized as the extension of the finite spectrum assignment of linear retarded systems. Effectiveness of the method is tested by illustrative examples.

Computation of quadratic cost functionals for linear systems with non-commensurate time delays

A method of evaluating quadratic cost functional for linear systems with non-commensurate time delays is presented. The main computational tasks involved in the method include the solution of a symbolic Diaphontine equation by Euclidean algorithm and the factorization of a finite-degree polynomial. As compared with an existing general method, the proposed one is more efficient in computing cross-covariances or gradients of quadratic cost functionals with respect to a decision variable. An example illustrating the numerical implementation of the proposed method is presented.

Finite spectrum assignment for nonlinear systems with non-commensurate delays

In this paper single input nonlinear systems with non-commensurate timedelays in state variables are considered. The objective is to design a coordinates transformation and a feedback which yield a finite dimensional linear controllable closed-loop system in a new coordinates, whose spectrum is located at an arbitrarily preassigned set of n points in the complex plane. An algebraic design procedure for this problem is proposed here. The proposed method is related to the exact linearization technique for systems with a finite dimension, and recognized as the extension of the finite spectrum assignment of linear retarded systems.

Finite Spectrum Assignment for Linear Systems With Non-Commensurate Time-Delays

This paper presents a new finite spectrum assignability condition for linear scalar systems with non-commensurate time-delays by a class offinite Laplace transforms ofall exponential functions corresponding to delay-times in a plant. The result is based on the Bezout equation and on a new coprimeness over multivariable polynomial matrices.

Numerical Computation of Cross-Covariance Functionals for Linear Systems With Multiple Time Delays

The problem of evaluating a cross-covariance functional of the form 12πi∫-i∞i∞F(s)G(-s)ds arises, e.g., in parametric optimization oflinear systems and in optimal linear filtering. In this paper, an algorithm is presented for computing cross-covariance functionals for linear systems with multiple commensurate time delays. The algorithm is based on converting a crosscovariance functional into an equivalent auto-covariance one. Then by utilizing an existing partialfraction-expansion scheme for a class of two-dimensional rational transfer functions, the evaluation ofa cross-covariance functional is reduced to the determination ofsymbolic inversion ofa polynomial matrix and the spectral factorization of a finite-degree real-coefficient polynomial. It is shown that the presented algorithm can be extended to systems having non-commensurate time delays through either introducing fictitious delays or adjusting time delays with rational approximation such that the resulted delays are commensurate. In order to illustrate the effectiveness of the algorithm, an example is provided.

α-Stability analysis of perturbed systems with multiple noncommensurate time delays

In terms of the fundamental matrix and the Jordan canonical form of the system matrix A/sub 0/, a new and simple /spl alpha/-stability criterion for multiple noncommensurate time-delay systems is proposed. The criterion is sufficient to ensure that all roots of the system's characteristic equation lie to the left of Re(s)=-/spl alpha/, /spl alpha//spl ges/0 and is also extended to the delay systems with parametric perturbations. It will be seen that if /spl alpha/ is not equal to zero, the corresponding stability criteria depend on the delay time.

A new approach for the robust stability of perturbed systems with a class of noncommensurate time delays

In this paper, based on the Lyapunov stability theorem, matrix measure, and norm inequalities, a new approach for the robust stability of perturbed systems with a class of noncommensurate time delays is presented. Two classes of linear parametric perturbations are treated: (1) unstructured; and (2) highly structured perturbations. Several concise sufficient conditions, delay-dependent or delay-independent, are proposed to guarantee the asymptotic stability and positive stability degree of the perturbed multiple time-delay systems. Finally, two numerical examples are given to demonstrate the applications of these quantitative results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

複数のむだ時間を含む系の有限極配置に関する一考察

複数のむだ時間を含む系の有限極配置に関する一考察

複数個のむだ時間を含む1入出力系の有限極配置

複数個のむだ時間を含む1入出力系の有限極配置

Robust stability of uncertain time-delay systems

This paper presents several sufficient conditions, delay-independent or delay-dependent, that guarantee the robust stability of uncertain time-delay systems subjected to parametric perturbations. Both single and composite uncertain systems with one delayed state are considered and each of these results, expressed by a succinct scalar inequality, permits the assessment of the transient behaviour of uncertain systems. The robustness of the time-delay system with respect to delay uncertainty is also discussed. Furthermore, these results are extended to the perturbed systems with multiple non-commensurate time delays. It is shown that the parameter perturbations may destabilize the system; hence the nominal system should be sufficiently stable to ensure robust stability.

Stabilization of time-delay systems using finite-dimensional compensators

For linear time-invariant systems with one or more noncommensurate time delays, necessary and sufficient conditions are given for the existence of a finite-dimensional stabilizing feedback compensator. In particular, it is shown that a stabilizable time-delay system can always be stabilized using a finite-dimensional compensator. The problem of explicitly constructing finite-dimensional stabilizing compensators is also considered.

Pointwise stability and feedback control of linear systems with noncommensurate time delays

Feedback control of linear neutral (and retarded) time-delay systems with one or more non-commensurate time delays is studied. A new (algebraic) notion of stability, called pointwise stability, is defined and is shown to be generically equivalent to uniform asymptotic stability independent of delay. Necessary and sufficient conditions are then given for regulability, that is, for the existence of a dynamic output feedback compensator with pure delays such that the closed-loop system is internally pointwise stable (and thus stable independent of delay). Necessary and sufficient conditions involving matrix-fraction descriptions are also given for the existence of a state realization which is regulable. Finally, the problem of stabilization using nondynamic state feedback is briefly considered in the case when the system's input matrix has constant rank.

Sufficient conditions for instability of delay differential systems

The paper gives sufficient conditions for instability of linear systems of both the neutral and retarded types with commensurate and non-commensurate time delays. The conditions are given in terms of time delays and coefficients of the characteristic quasi-polynomials of these systems. Illustrative examples are presented.