Linear Time-invariant Uncertainty Research Articles

Robustness analysis of linear periodic time-varying systems subject to structured uncertainty

In this paper, we show how Floquet theory may be combined with a technique known as Lifting to cast a linear periodically time-varying system subject to structured linear time invariant uncertainty in the form of a linear fractional transformation. The stability and performance robustness of the resulting system may then be analysed using standard μ -analysis methods. A significant advantage of the proposed approach is that it allows the computation of a worst-case destabilising uncertainty combination which may be used to estimate the conservatism of the computed robustness margin. An example is given to illustrate the application of the proposed approach.

An algorithm for sampling subsets of H/sub /spl infin// with applications to risk-adjusted performance analysis and model (in)validation

In spite of their potential to reduce computational complexity, the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty, since the problem of sampling causal bounded operators is largely open. In this note, we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of H/sub /spl infin//. As we show in the note, samples taken from these sets can be used to carry out model (in)validation and robust performance analysis in the presence of structured dynamic linear time-invariant uncertainty, problems known to be NP-hard in the number of uncertainty blocks.

Convex Necessary and Sufficient Conditions for Frequency Domain Model (In)Validation Under SLTV Structured Uncertainty

This paper deals with the problem of model (in)validation of discrete time, causal, linear time-invariant (LTI) stable models subject to slowly linear time-varying structured uncertainty, using frequency domain data corrupted by additive noise. It is well known that in the case of structured LTI uncertainty the problem is NP hard in the number of uncertainty blocks. The main contribution of this paper shows that, on the other hand, if one considers arbitrarily slowly time varying uncertainty and noise in L/sub 2/, then tractable, convex necessary and sufficient conditions for (in)validation can be obtained. Additional results include a discussion of the case where the noise is characterized in terms of the L/sub /spl infin// norm.

Lyapunov functionals in complex μ analysis

Conditions for robust stability of linear time-invariant systems subject to structured linear time-invariant uncertainties can be derived in the complex /spl mu/ framework, or, equivalently, in the framework of integral quadratic constraints. These conditions can be checked numerically with linear matrix inequality (LMI)-based convex optimization using the Kalman-Yakubovich-Popov lemma. We show how LMI tests also yield a convex parametrization of (a subset of) Lyapunov functionals that prove robust stability of such uncertain systems. We show that for uncertainties that are pure delays, the Lyapunov functionals reduce to the standard Lyapunov-Krasovksii functionals that are encountered in the stability analysis of delay systems. We demonstrate the practical utility of the Lyapunov functional parametrization by deriving bounds for a number of measures of robust performance (beyond the usual H/sub /spl infin// performance); these bounds can be efficiently computed using convex optimization over linear matrix inequalities.

Robust synthesis of feedforward compensators

The design of a feedforward compensator for robust /spl Hscr//sub /spl infin// or /spl Hscr//sub 2/ performance under structured uncertainty is considered. For linear time-invariant uncertainty, a convex method based on linear matrix inequalities (LMIs) across the frequency variable is given. For nonlinear or time-varying perturbations and /spl Hscr//sub /spl infin// performance, the design problem is reduced exactly to a state-space LMI, and extensions to /spl Hscr//sub 2/ performance are discussed. An example illustrates the application of these techniques to two-degree-of-freedom control design.

Small-μ theorems with frequency-dependent uncertainty bounds

We present conditions, some necessary and some sufficient, valid under weak assumptions, for robust stability and uniform robust stability of uncertain linear time-invariant systems with linear time-invariant uncertainties that are block-diagonal, with known frequency-dependent norm bounds on the diagonal, blocks. Small-μ theorems with frequency-independent uncertainty bounds are recovered as special cases.

An IQC for uncertainty satisfying both norm-bounded and passivity constraints

This paper introduces a new integral quadratic constraint for describing a single block of dynamic, linear time-invariant uncertainty that simultaneously satisfies norm-bound and passivity constraints. For the associated matrix uncertainty problem, we give an upper bound on the quantitative stability indicator μ and state conditions under which this bound is tight.

Analysis of Robust H2 Performance Using Multiplier Theory

In this paper, the problem of determining the worst-case H2 performance of a control system subject to linear time-invariant uncertainties is considered. A set of upper bounds on the performance is derived, based on the theory of stability multipliers and the solution of an original optimal control problem. The numerical issues raised by the resulting computational problems are discussed; in particular, newly developed interior-point convex optimization methods, combined with linear matrix inequalities, apply very well to the fast and accurate solution of these problems. The new results compare favorably with prior ones. The method can be extended to other types of perturbations.