Stability Of Discrete-time Linear Systems Research Articles

Stability of linear discrete-time systems: geometric considerations

Stability of linear discrete-time systems: geometric considerations

Stabilization of discrete-time linear systems with a time delay in the feedback loop

A discrete-time, linear, time-invariant control system with a fixed time delay in the feedback loop is considered. We investigate the problem of feedback stabilization and present some general criteria. Simple necessary and sufficient conditions for stabilization, which take the form of algebraic inequalities involving the system parameters, are developed for time delays whose values do not exceed 2, as well as for one-dimensional systems with an arbitrary time delay.

Extended power method and stability of linear discrete-time systems

A computationally simple and efficient method is proposed to determine the stability of linear discrete-time systems. The method directly utilises the system (state-transition) matrix and avoids the evaluation of the characteristic polynomial. Another interesting feature of this approach is that it can be extended to extract the eigenvalues of matrices, in a recursive fashion.

Optimal infinite-horizon control and the stabilization of linear discrete-time systems: State-control constraints and nonquadratic cost functions

Stability results are given for a class of feedback systems arising from the regulation of time-invariant, discrete-time linear systems using optimal infinite-horizon control laws. The class is characterized by joint constraints on the state and the control and a general nonlinear cost function. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee asymptotic stability of the optimal feedback systems. Prior results, which concern the linear quadratic regulator problem, are included as a special case. The proofs make no use of discrete-time Riccati equations and linearity of the feedback law, hence, they are intrinsically different from past proofs.

Stability of linear discrete-time systems

A computationally efficient and simple method is suggested for determining the stability of digital systems. The new method is then compared with other existing methods.

Some properties of the canonical parameter space

The canonical parameter space is symmetric. This simple result is used to extend several theorems on root location involving polynomials where only one class of polynomials is given. The smallest region containing polynomials with largest absolute-value zero of unity or less is derived. This leads to a simple proof for the strongest sufficient condition for the stability of linear discrete-time systems using absolute norms.

A note on stability and lattice filter relations

In this note we draw attention to an earlier result by Marden [2] for establishing the stability of linear discrete-time systems. The stability algorithm then provides a simple constructive realization of stable filters in lattice form. The class of unstable filters which cannot be represented in lattice form is also partially characterized.

A direct Routh stability method for discrete system modelling

The Routh approximation method which has been suggested for the reduction of stable discrete time linear systems to guarantee stable models, uses the bilinear transformation. A stability theorem in the z-plane is presented which is shown to be an equivalent of the Routh criterion. An efficent method that avoids the bilinear transformation is presented by which the Routh disrete models are derived directly in the z-plane.

不規則に変動するむだ時間を含む線形離散時間系の安定性

不規則に変動するむだ時間を含む線形離散時間系の安定性

The use of second-order information in the approximation of discreate-time linear systems

It is common practice to partially characterize a filter with a finite portion of its impulse response, with the objective of generating a recursive approximation. This paper discusses the use of mixed first and second information, in the form of a finite portion of the impulse response and autocorrelation sequences. The discussion encompasses a number of techniques and algorithms for this purpose. Two approximation problems are studied: an interpolation problem and a least squares problem. These are shown to be closely related. The linear systems which form the solutions to these problems are shown to be stable. An efficient algorithm for obtaining solutions is given and shown to be closely related to a well-known algorithm of Levinson and the Jury stability test. The close connection between these algorithms suggests that they are fundamental in the numerical analysis of stable discrete-time linear systems.

Application of the Routh array to stability of discrete-time linear systems

It is shown that a Routh-type array can be applied to the problem of location of zeros of a real polynomial with respect to the unit disc. This is done by obtaining new half-order expressions for the Schur-Cohn determinants. The work is complementary to that in a previous paper in which it was shown that a generalization of the Jury array can be similarly applied to the continuous-time linear system stability problem.

On the stability of linear discrete-time systems

In Anderson a connection of two types of stability: Liapunov stability, reflecting the internal stability of a system, and bounded-input bounded-output stability, reflecting the external stability of a system, has been established for time-varying linear finite-dimensional dynamic systems which may be represented in a special canonical form. This correspondence extends the connection to time-varying linear finite-dimensional discrete-time systems.