Xiaoru Niu

Stability robustness of linear discrete-time systems in the presence of uncertainty

The stability robustness problem is considered for nominally stable linear discrete-time systems. Using time-domain analysis methods and Lyapunov theory, bounds on the norms of the time-varying (non-)linear perturbations are given, to maintain the asymptotic stability of these systems in the presence of such perturbations.

Improved bounds for linear discrete-time systems with structured perturbations

A time-domain analysis of the stability robustness of linear discrete-time systems subject to time-varying structured perturbations is considered. The Lyapunov stability theory is used to obtain bounds on the perturbation such that the systems remain stable. It is shown that these bounds are less conservative than the existing ones. This is illustrated via two numerical examples. >

Optimization of stability robustness bounds for linear discrete-time systems

In this paper, existing stability robustness measures for the perturbation of both continuous-time and discrete-time systems are reviewed. Optimized robustness bounds for discrete-time systems are derived. These optimized bounds are obtained reducing the conservatism of existing bounds by (a) using the structural information on the perturbation and (b) changing the system coordinates via a properly chosen similarity transformation matrix. Numerical examples are used to illustrate the proposed reduced conservatism bounds.

New robustness bounds for discrete systems with random perturbations

Some new stochastic stability robustness bounds for state-space models are reported. Nominally exponentially stable discrete-time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness. The methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one. The results are compared with each other and with the exact stability region in an example. >

New Results on the Robustness of Discrete-Time Systems with Stochastic Perturbations

Enin Yaz Electrical Engineerg Department University of Arkansas Fayetteville, AR 7270

Robustness analysis for real-time simulation

A stability bound for linear continuous systems subject to nonlinear perturbations is derived. This bound guarantees that systems being simulated using two-step integrators remain stable under such perturbations. A numerical example is used to illustrate the effect of the sampling time on the bound

Robustness considerations for p-step matrix integrators with uncertainty in the continuous system mode

Abstract Robustness measures for p-step matrix integrators are established. These measures are the quantitative bounds for either structured or unstructured perturbations existing in continuous-time systems to ensure that discrete versions of those systems obtained using p-step matrix integrators remain stable. Examples are given to illustrate the usefulness of the proposed measures. The effect of the sampling time T, the choice of the discretizing scheme, and the integrator step size on these robustness measures is discussed through examples.

Robustness analysis of two-step integrators with uncertainty in the system model

Abstract Quantitative bounds for the nonlinear perturbation of linear time-invariant continuous-time systems simulated using two-step matrix integrators are obtained. These bounds ensure that systems being simulated using two-step integrators remain stable under such perturbations. The effect of the sampling time T on the bounds is investigated via numerical examples.

Robustness measures for discrete-time systems with deterministic and stochastic perturbations

The stability robustness problem for nominally stable linear discrete-time systems is considered. Upper bounds on the deterministic and stochastic structural perturbation with dependent variation are obtained by using the time-domain approach and Lyapunov stability theory. These bounds guarantee that the stability of discrete-time systems subject to these types of perturbations is maintained.<<ETX>>

Analysis and optimization of stability robustness bounds for discretized systems

In this paper, robustness bounds for the perturbations of continuous-time systems to ensure the stability of their discretized counterparts are developed. Both zero-order hold and P-step matrix integrators are considered. The effect of the sampling time on the robustness bounds is studied via examples. To determine how well a simulated system will retain the robustness properties of the continuous-time system being simulated, a new criterion for the selection of the simulation method and time step is introduced. Both implicit and explicit robustness measures for sampled-data systems are obtained.