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Linear Time-invariant Systems (linear + time-invariant_system)

Distribution by Scientific Domains

Engineering	92%

Selected Abstracts

On robust stability of uncertain systems with multiple time-delays

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2010
Tong ZhouArticle first published online: 27 NOV 200
Abstract On the basis of an infinite to one mapping and the structure of the null space of a multivariate matrix polynomial (MMP), a novel sufficient condition is derived in this paper for the robust stability of a linear time-invariant system with multiple uncertain time-delays, parametric modelling errors and unmodelled dynamics. This condition depends on time-delay bounds and is less conservative than the existing ones. An attractive property is that this condition becomes also necessary in some physically meaningful situations, such as the case that there is only one uncertain time-delay and neither parametric perturbations nor unmodelling errors exist. Moreover, using ideas of representing a positive-definite MMP through matrix sum of squares, an asymptotic necessary and sufficient condition is derived for the robust stability of this system. All the conditions can be converted to linear matrix inequalities. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Perfusion parameters derived from bolus-tracking perfusion imaging are immune to tracer recirculation,

JOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 3 2010
Jayme Cameron Kosior PhD
Abstract Purpose: To investigate the impact of tracer recirculation on estimates of cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT). Materials and Methods: The theoretical model used to derive CBF, CBV, and MTT was examined. CBF and CBV estimates with and without tracer recirculation were compared in computer simulations to examine the effects of tracer recirculation. Results: The equations used to derive CBF, CBV, and MTT assume that the arterial input function and tissue tracer signals define the input and output signals, respectively, of a linear time-invariant system. As a result of the principle of superposition, these perfusion parameters are immune to tracer recirculation, which was confirmed by computer simulation. However, limited acquisition durations can lead to CBV and CBF errors of up to 50%. Conclusion: Tracer recirculation does not impact estimation of CBF, CBV, or MTT. However, previous approaches used to remove recirculation effects may be beneficial when used to compensate for limited acquisition durations in which the passage of the bolus is not adequately captured. J. Magn. Reson. Imaging 2010;31:753,756. © 2010 Wiley-Liss, Inc. [source]

A novel approach for root distribution analysis of linear time-invariant systems using Routh and Fuller tables

ASIAN JOURNAL OF CONTROL, Issue 3 2009
S. N. Sivanandam
Abstract The root distribution of a given characteristic equation of a linear time-invariant system can be analyzed with the help of a Routh table using the elements of the first column in the table. In the case of unstable systems, sometimes, a zero element may appear in the third row of the first column of the Routh array. This prematurity can be suitably handled as indicated by various authors. In this paper, the given characteristic polynomial having roots in the right hand plane is multiplied by a suitable polynomial, and Routh and Fuller tables are applied for the resultant polynomial to infer the complete root distribution. Further, the column polynomials from each table are adopted to know more about root distribution, which forms the core of the proposed work. The Routh table helps in counting and locating roots in the s -plane, and the Fuller table helps in depicting whether the roots are distinct or complex in nature. In this regard, it is shown in this paper that the simultaneous integration of Routh and Fuller tables yields a good amount of information regarding the root distribution in the s -plane. The newly presented procedure is illustrated with examples. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Robust multiple-fault detection and isolation: A gradient flow approach

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 8 2008
Alessandro Casavola
Abstract This paper presents a novel solution to the fault detection and isolation observer design problem for linear time-invariant systems. A gradient flow approach is proposed for synthesizing a residual generator under optimal eigenstructure assignment. This is achieved by minimizing the spectral condition number of the observer eigenvector matrix. The properties of convergence of the gradient flow solution are proved and its efficiency demonstrated via a numerical example. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Direct adaptive command following and disturbance rejection for minimum phase systems with unknown relative degree

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2007
Jesse B. Hoagg
Abstract This paper considers parameter-monotonic direct adaptive command following and disturbance rejection for single-input single-output minimum-phase linear time-invariant systems with knowledge of the sign of the high-frequency gain (first non-zero Markov parameter) and an upper bound on the magnitude of the high-frequency gain. We assume that the command and disturbance signals are generated by a linear system with known characteristic polynomial. Furthermore, we assume that the command signal is measured, but the disturbance signal is unmeasured. The first part of the paper is devoted to a fixed-gain analysis of a high-gain-stabilizing dynamic compensator for command following and disturbance rejection. The compensator utilizes a Fibonacci series construction to control systems with unknown-but-bounded relative degree. We then introduce a parameter-monotonic adaptive law and guarantee asymptotic command following and disturbance rejection. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2002
Robert N. Shorten
In this paper, necessary and sufficient conditions are derived for the existence of a common quadra-tic Lyapunov function for a finite number of stable second order linear time-invariant systems. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A robust fault detection and isolation filter design under sensitivity constraint: An LMI approach

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2008
Saverio Armeni
Abstract This paper deals with the design of a residual generator (RG) for linear time-invariant systems subject to simultaneous different faults, disturbances and measurement noises. The objective is to design an RG filter that maximizes the transmission from a potential fault to a related residual, while minimizing the ones from nuisances (disturbances, measurement noises and other faults). The isolation of each fault is carried out by designing a bank of RG filters, each one insensitive, as much as possible, to nuisances and capable of detecting the occurrence of its related fault. The design is carried out through ,, filtering techniques under an eigenstructure assignment constraint. Under mild assumptions, the RG filter can be obtained by solving a ,-parameterized linear matrix inequality optimization problem. A comparison with existing fault detection and isolation (FDI) methods is considered in order to exhibit the relative merits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

New results for the analysis of linear systems with time-invariant delays

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2003
Jianrong Zhang
Abstract This paper presents a comparison system approach for the analysis of stability and ,, performance of linear time-invariant systems with unknown delays. The comparison system is developed by replacing the delay elements with certain parameter-dependent Padé approximations. It is shown using the special properties of the Padé approximation to e,s that the value sets of these approximations provide outer and inner coverings for that of each delay element and that the robust stability of the outer covering system is a sufficient condition for the stability of the original time delay system. The inner covering system, in turn, is used to provide an upper bound on the degree of conservatism of the delay margin established by the sufficient condition. This upper bound is dependent only upon the Padé approximation order and may be made arbitrarily small. In the single delay case, the delay margin can be calculated explicitly without incurring any additional conservatism. In the general case, this condition can be reduced with some (typically small) conservatism to finite-dimensional LMIs. Finally, this approach is also extended to the analysis of ,, performance for linear time-delay systems with an exogenous disturbance. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A comparison of small gain versus Lyapunov type robust stability bounds

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2001
Jie Chen
Abstract We address stability issues pertaining to perturbed linear time-invariant systems described by state space models. We show that for a class of highly structured uncertainties in the system matrix, a robust stability bound given by the complex structured singular value is less conservative than that obtained via Lyapunov approach. This result thus provides a counterpart to an earlier one pertaining to unstructured uncertainties, and serves to extend and support the statement that frequency domain small gain conditions may often be less conservative than those time domain criteria obtained using Lyapunov approach. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A novel approach for root distribution analysis of linear time-invariant systems using Routh and Fuller tables

On ,, model reduction for discrete-time linear time-invariant systems using linear matrix inequalities,

ASIAN JOURNAL OF CONTROL, Issue 3 2008
Yoshio Ebihara
Abstract In this paper, we address the ,, model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the ,, optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting. [source]

Convergence and Robustness of Iterative Learning Control For Strongly Positive Systems

ASIAN JOURNAL OF CONTROL, Issue 1 2002
Daniel Andres
ABSTRACT In this paper, we consider the convergence and robustness of a general iterative learning control scheme for a class of systems which we term "strongly positive". The analysis is made in the framework of Hilbert-space theory. Thus the results are valid for discrete-time as well as continuous-time systems which may be time-variant or time-invariant. For the special case of continuous linear time-invariant systems which are defined over the Hilbert-space of square integrable functions, we will give a characterization of strongly positive systems in the frequency domain. [source]

Discrete-Time Risk-Sensitive Filters with Non-Gaussian Initial Conditions and Their Ergodic Properties

ASIAN JOURNAL OF CONTROL, Issue 4 2001
Subhrakanti Dey
ABSTRACT In this paper, we study asymptotic stability properties of risk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risk-sensitive filter asymptotically converges to a suboptimal filter initialized with an incorrect covariance matrix for the initial state vector in the mean square sense provided the incorrect initializing value for the covariance matrix results in a risk-sensitive filter that is asymptotically stable, that is, results in a solution for a Riccati equation that is asymptotically stabilizing. For non-Gaussian initial conditions, we derive the expression for the risk-sensitive filter in terms of a finite number of parameters. Under a boundedness assumption satisfied by the fourth order absolute moment of the initial state variable and a slow growth condition satisfied by a certain Radon-Nikodym derivative, we show that a suboptimal risk-sensitive filter initialized with Gaussian initial conditions asymptotically approaches the optimal risk-sensitive filter for non-Gaussian initial conditions in the mean square sense. Some examples are also given to substantiate our claims. [source]