Class Of Linear Time-varying Systems Research Articles

A numerical technique for the stability analysis of linear switched systems

In this paper the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a polyhedral Lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms. The technique can be used to prove the stability of switched linear systems, classes of linear time-varying systems and linear differential lnclusions. We also present preliminary results on another related problem; namely, the construction of multiple polyhedral Lyapunov functions for the specification of stabilizing switching sequences for a switched system constructed from a family of stable linear subsystems.

Robust stability of a class of linear time-varying systems

This paper firstly considers the exponential stability of unforced linear systems of slowly time-varying dynamics. Possible switchings of the system structure to unstable dynamics during certain finite time intervals are admitted. The maintenance of global exponential stability does not necessarily require at most a finite number of switchings in the dynamics while infinitely many switches can also lead to stability. The mechanism to achieve stability under infinitely many switches in the dynamics is to maintain the system in the stable region during time intervals of sufficiently large length without switches provided that the system dynamics evolves at a sufficiently small rate with time. Special attention is paid to the robust tolerance to a class of state disturbances and to the case of a time-varying matrix of dynamics that possess either piecewise constant or constant eigenvalues. The obtained results can be relevant for their use in stability issues for the cases of multimodel non-adaptive and adaptive control with improved transient performances.

Overlapping Quadratic Optimal Control of Linear Time-Varying Commutative Systems

Overlapping quadratic optimal control of linear time-invariant continuous-time systems by using generalized selection of complementary matrices has been recently developed as a powerful and effective means of decentralized control design of linear time-invariant systems. In this paper, it is shown that similar generalizations exist for linear time-varying systems. The results presented here concern implicit conditions for a general form of the transition matrices and explicit conditions for a commutative class of linear time-varying systems. Several important large classes of complementary matrices are selected to offer computationally attractive results. The effectiveness of this generalized selection scheme is illustrated by a numerical example of overlapping decentralized control design.

Generalised minimum variance control of linear time-varying systems

The problem of generalised minimum variance control of linear time-varying discrete-time systems is studied. Standard time-varying controlled autoregressive moving average models are considered, and the sum of plant output tracking error variance plus a penalty term on plant input is chosen as the cost functional. The time-varying controller described is able to minimise the generalised tracking error variance and guarantees closed-loop exponential stability for a large class of linear time-varying systems, including plants which have long time delays and are not stably invertible.

Stabilization of a class of linear time-varying systems via modeling error compensation

The aim of this paper is to show that modeling error compensation techniques can be extended for the case of single-input/single-output minimum-phase, linear time-varying systems whose parameters can drift arbitrarily fast.

Time-varying linear systems and input-output stability

One useful strategy for establishing input–output stability is to seek conditions on the system map so that a certain lower-bound condition is met. We show here that, for a large class of time-varying linear systems, the lower-bound condition for stability is in fact necessary. Copyright © 2000 John Wiley & Sons, Ltd.

A generalised predictive controller for linear time-varying systems

This paper studies the problem of predictive control of time-varying linear systems and develops a generalised predictive controller based on a standard rime-varying autoregressive moving average model. The controller allows various control and output horizons and is applicable to a large class of time-varying linear systems. It is an extension of The previous results on the minimum variance prediction and control of time-varying linear systems based on pseudocommutation.

Linear adaptive robust controllers for a class of uncertain dynamical systems with unknown bounds of uncertainties

The problem of robust stabilization of a class of linear time-varying systems with disturbance and uncertain parameters is considered. The bounds of the disturbance and uncertain parameters are assumed to be unknown. For such uncertain dynamical systems, a class of linear continuous adaptive robust state feedback controllers are proposed. It is shown that the resulting closed-loop systems are stable in the sense of uniform ultimate houndedness. A numerical example is given to demonstrate the synthesis procedure for the proposed adaptive stabilizing state feedback controller.

On the eigenstructure of linear quasi-time-invariant systems

In this paper, the eigenstructure of a class of linear time-varying systems, termed linear quasi-time-invariant (LQTI) systems, is investigated. A system composed of dynamic devices such as linear time-varying capacitors and resistors can be an example of the class. To describe and analyze the LQTI systems effectively, a differential operator G composed of the derivative operator D and some time functions is adopted. Then, the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characterisics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. The corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency-domain analysis and design of the filters. It is also noted that the stability is determined by the position of poles in the G frequency domain, where the stable region in the complex plane is different from the classical left half s plane. A point in the extended Laplace transform space represents a complex exponential function modulated by some functions. As an application example, an LQTI filter is examined and designed by using the concept of eigenstructure of LQTI system. Also, a new type of modulation or frequency shift property is examined as in the linear time-invariant filter theory.

Minimum-variance control of linear time-varying systems

We study the problem of minimum-variance control of linear time-varying discrete-time systems. We consider the standard time-varying controlled autoregressive moving-average model and develop a time-varying controller that guarantees both closed-loop stability and minimum-variance output control for a large class of linear time-varying systems. The controller is based on our previous results on minimum-variance prediction for linear time-varying systems. We also show that the standard minimum-variance controller cannot in general guarantee closed-loop stability when applied to linear time-varying systems. However, a simple modification can make the closed loop stable.

Analysis of practical stability and Lyapunov stability of linear time-varying neutral delay systems

Practical stability guarantees trajectories of a dynamical system being bounded within a prespecified region during a specified time interval and is of great interest in many applications. For a class of linear time-varying systems described by delay differential equations of neutral type, concepts of practical stability involving both variations of the state and its derivative are introduced in terms of given estimate sets. Sufficient conditions of practical stability are established on the basis of the mixed differential difference comparison principle presented in this paper, in terms of coefficients of the systems and the given allowable trajectory bounds. For the case of time-invariant estimate sets, these conditions are also independent of delay. These results are then applied to the Lyapunov stability and positively invariant tubes of the corresponding homogeneous systems. Specifically, an algebraic condition of globally exponentially asymptotical stability is derived, which is related to the well known property of the M-matrix and is independent of delay. Finally, an illustrative example is given.

Minimum variance prediction for linear time-varying systems

In this paper we study the problem of minimum variance prediction for linear time-varying systems. We consider the standard time-varying autoregression moving average (ARMA) model and develop a predictor which guarantees minimum variance prediction for a large class of linear time-varying systems. The predictor is developed based on a pseudocommutation technique for dealing with noncommutativity of linear time-varying operators in a transfer operator framework. We also show connections between this input-output predictor and the Kalman predictor via an example.

Robust detection filter design in the presence of time-varying system perturbations

This paper discusses the problem of designing detection filters for a class of linear time-varying systems. The basic contribution of the paper is that by, applying a time-invariant equivalent representation of the original time-varying system, it is possible to construct a detection filter such that the solution of the design problem can be solved using algebraic methods and geometric concepts similar to the case of time invariant situations.

A convex characterization of gain-scheduled H/sub ∞/ controllers

An important class of linear time-varying systems consists of plants where the state-space matrices are fixed functions of some time-varying physical parameters /spl theta/. Small gain techniques can be applied to such systems to derive robust time-invariant controllers. Yet, this approach is often overly conservative when the parameters /spl theta/ undergo large variations during system operation. In general, higher performance can be achieved by control laws that incorporate available measurements of /spl theta/ and therefore "adjust" to the current plant dynamics. This paper discusses extensions of H/sub /spl infin// synthesis techniques to allow for controller dependence on time-varying but measured parameters. When this dependence is linear fractional, the existence of such gain-scheduled H/sub /spl infin// controllers is fully characterized in terms of linear matrix inequalities. The underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available. The formalism and derivation techniques developed here apply to both the continuous- and discrete-time problems. Existence conditions for robust time-invariant controllers are recovered as a special case, and extensions to gain-scheduling in the face of parametric uncertainty are discussed. In particular, simple heuristics are proposed to compute such controllers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Minimum Variance Prediction for Linear Time-Varying Systems

In this paper we study the problem of minimum variance prediction for linear time- varying systems. We consider the standard time-varying ARMA model and develop a predictor which guarantees minimum variance prediction for a large class of linear time-varying systems. We also show equivalence between this input-output predictor and the Kalman predictor using an example. A simulation result is also included.

036 Observers with asymptotic gain for a class of linear time-varying systems with singularity

036 Observers with asymptotic gain for a class of linear time-varying systems with singularity

Stabilität einer Klasse zeitvarianter linearer Systeme/Stability of a class of time-varying linear systems

Article Stabilität einer Klasse zeitvarianter linearer Systeme/Stability of a class of time-varying linear systems was published on December 1, 1993 in the journal at - Automatisierungstechnik (volume 41, issue 3).

Observers with Asymptotic Gain for a Class of Linear Time-varying Systems with Singularity

We present a sufficient condition for the existence of an observer with asymptotic gain, namely with a constant gain when the system is expressed in terms of its fastest time-scale. This condition crucially depends on the concept of asymptotic observability. When this property does not hold, an observer with asymptotic gain may not exist whereas observers defined on a finite horizon may be well defined.

On vibrations of a class of linear time-varying systems

A class of dynamic multi-degree-of-freedom systems with time-varying parameters has been studied. The systems have been assumed to vary during a limited time interval and to remain invariant outside of this interval. The exciting forces have been assumed to be periodic. Several analytical interpretations of the system responses have been considered. Applications to machine condition monitoring have been discussed. Methods of identification of the shape of the functions, describing the parameter variation as well as methods of identification of the relative intensity of the changes of individual parameters, have been developed. The identification techniques have been based on a realistic assumption that the exciting forces are unknown and that the responses of the system are available.

Equivalent characterizations of detectability and stabilizability for a class of linear time-varying systems

This paper addresses four characterizations of detectability and stabilizability for a broad class of linear continuous-time time-varying systems. It is shown that for the class of constant-rank systems all these notions of detectability and stabilizability are actually equivalent to each other.