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Linear Time-varying Systems (linear + time-varying_system)
Selected AbstractsAdaptive/robust time-varying stabilization of second-order non-holonomic chained form with input uncertaintiesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2002B. L. Ma Abstract Adaptive and robust time-varying control schemes are constructed to stabilize second-order non-holonomic chained form in the presence of input uncertainties. The proposed control schemes guarantee that all the state variables converge to zero asymptotically in spite of input uncertainties, and are applied to the stabilization of a planar rigid body driven by active force and torque with unknown inertia and geometric parameters. The basic idea of the proposed stabilization schemes is to first convert the non-holonomic system into a linear time-varying form by time-varying co-ordinate transformation, and then design control laws to stabilize the converted linear time-varying system. Copyright © 2002 John Wiley & Sons, Ltd. [source] Delay dependent stabilization of linear time-varying system with time delayASIAN JOURNAL OF CONTROL, Issue 5 2009S. Sh. Abstract This paper investigates both stability and stabilization dependent on the delay of a class of time-varying linear systems with a constant point time delay. The matrices, describing the state space dynamics, are parameterized by time-varying function matrices. A numerical example is given in order to verify the theoretical results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] A test for stability robustness of linear time-varying systems utilizing the linear time-invariant ,-gap metricINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2009Wynita M. Griggs Abstract A stability robustness test is developed for internally stable, nominal, linear time-invariant (LTI) feedback systems subject to structured, linear time-varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI ,-gap metric framework. The scaled LTI ,-gap metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI ,-gap metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. Copyright © 2008 John Wiley & Sons, Ltd. [source] Stability of Linear Parameter Varying and Linear Switching SystemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Fabian Wirth We consider stability of families of linear time-varying systems, that are determined by a set of time-varying parameters which adhere to certain rules. The conditions are general enough to encompass on the one hand stability questions for systems that are frequently called linear parameter varying systems in the literature and on the other hand also linear switching systems, in which parameter variations are allowed to have discontinuities. Combinations of these two sets of assumptions are also possible within the framework studied here. Under the assumption of irreducibility of the sets of system matrices, we show how to construct parameter dependent Lyapunov functions for the systems under consideration that exactly characterize the exponential growth rate. It is clear that such Lyapunov functions do not exist in general. But every system of our class can be reduced to a finite number of subsystems for which irreducibility holds. [source] Reduced-order state estimation for linear time-varying systems,ASIAN JOURNAL OF CONTROL, Issue 6 2009In Sung Kim Abstract We consider reduced-order and subspace state estimators for linear discrete-time systems with possibly time-varying dynamics. The reduced-order and subspace estimators are obtained using a finite-horizon minimization approach, and thus do not require the solution of algebraic Lyapunov or Riccati equations. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Chemical networks with inflows and outflows: A positive linear differential inclusions approachBIOTECHNOLOGY PROGRESS, Issue 3 2009David Angeli Abstract Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source] | ||||||||||