Showing papers by "Minyue Fu published in 1997"

A linear matrix inequality approach to robust H/sub /spl infin// filtering

Abstract: We consider the robust H/sub /spl infin// filtering problem for a general class of uncertain linear systems described by the so-called integral quadratic constraints (IQCs). This problem is important in many signal processing applications where noise, nonlinearity, quantization errors, time delays, and unmodeled dynamics can be naturally described by IQCs. The main contribution of this paper is to show that the robust H/spl infin/ filtering problem can be solved using linear matrix inequality (LMI) techniques, which are numerically efficient owing to recent advances in convex optimization. The paper deals with both continuous and discrete-time uncertain linear systems.

A dual formulation of mixed /spl mu/ and on the losslessness of (D, G) scaling

Abstract: This paper studies the mixed structured singular value, /spl mu/, and the well-known (D,G)-scaling upper bound, /spl nu/. A dual characterization of /spl mu/ and /spl nu/ is derived, which intimately links the two values. Using the duals it is shown that /spl nu/ is guaranteed to be lossless (i.e. equal to /spl mu/) if and only if 2(m/sub r/+m/sub e/)+m/sub C//spl les/3, where m/sub r/, m/sub c/; and m/sub C/ are the numbers of repeated real scalar blocks, repeated complex scalar blocks, and full complex blocks, respectively. The losslessness result further leads to a variation of the well-known Kalman-Yakubovich-Popov lemma and Lyapunov inequalities.

The real structured singular value is hardly approximable

Abstract: This paper investigates the problem of approximating the real structured singular value (real /spl mu/). A negative result is provided which shows that the problem of checking if /spl mu/=0 is NP-hard. This result is much more negative than the known NP-hard result for the problem of checking if /spl mu/ 0 (even exponential functions of n), unless NP=P. A similar statement holds for the lower bound of /spl mu/. Our result strengthens a recent result by Toker, which demonstrates that obtaining a sublinear approximation for /spl mu/ is NP-hard.

Delay-dependent closed-loop stability of linear systems with input delay: an LMI approach

Abstract: This paper focuses on the problem of computing a control law which maximizes (in a sub-optimal sense) the delay of the closed-loop system for a class of linear systems with delayed input. The delay is assumed to be a continuous bounded time-varying function. The analysis is given using two different approaches: the Razumikhin based method and a frequency-filtering based method.

Improved upper bounds for the mixed structured singular value

Abstract: In this paper, we take a new look at the mixed structured singular value problem, a problem of finding important applications in robust stability analysis. Several new upper bounds are proposed using a very simple approach which we call the multiplier approach. These new bounds are convex and computable by using linear matrix inequality (LMI) techniques. We show, most importantly, that these upper bounds are actually lower bounds of a well-known upper bound which involves the so-called D-scaling (for complex perturbations) and G-scaling (for real perturbations).

Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis

Abstract: Motivated by the current limitations of the existing algorithms for robustness analysis, in this paper we take a different direction which follows the so-called probabilistic approach. That is, we aim to estimate the probability that a control system with uncertain parameters q restricted to a box Q attains a certain level of performance /spl gamma/. Since this probability depends on the underlying density function f(q), we study the following question: What is a "reasonable" density function so that the estimated probability makes sense? To answer this question, we define two new worst-case criteria and prove that the uniform density function is optimal in both cases. In the second part of the paper, we turn our attention to a subsequent problem. That is, taking f(q) as the uniform density function, we estimate the size of the so-called "good" and "bad" sets. Roughly speaking, the good set contains the parameters q E Q that have performance level better than or equal to /spl gamma/ while the bad set is the set of parameters q /spl isin/ Q that have performance level worse than /spl gamma/. To estimate the size of both sets, sampling is required. Then, we give bounds on the minimum sample size to attain a given accuracy and confidence.

Localization based switching adaptive control for time-varying discrete time systems

Abstract: In this paper a new systematic switching control approach to adaptive stabilization of linear time-varying discrete-time systems is presented. This approach is based on a localization method, and is conceptually different from existing switching adaptive control schemes. A feature of the localization based method is that the control switching converges rapidly. By utilizing this fast speed of localization and the rate of admissible parameter variation, we provide conditions under which the closed-loop system can be exponentially stabilized.

Localization based switching adaptive controllers

Abstract: Many different types of adaptive or universal controllers", capable of dealing with a very broad range of linear time-invariant systems, have been proposed. One class of such controllers uses switching between a finite, or at least countable, number of fixed controllers until stability is detected. Such controllers are very attractive from a theoretical viewpoint, in providing stabilization and asymptotic performance for a broad class of plants. However, such controllers are also known to have very poor transient properties, due to the long time required to search for a stabilizing feedback. The key contribution of this paper is to introduce the "method of localization" which can greatly improve the speed of the search. The method is described for linear time-invariant discrete time systems of known nominal order, with disturbances and noise present. Analysis and simulations demonstrate the potential for greatly improved transient performance.

Computational complexity of real structured singular value in ℓ p setting

Abstract: This paper studies the structured singular value (μ) problem with real parameters bounded by an l p norm. Our main result shows that this generalized μ problem is NP-hard for any given rational number p ∊ [1, ∞], whenever k, the size of the smallest repeated block, exceeds 1. This result generalizes the known result that the conventional μ problem (with p − ∞) is NP-hard. However, our proof technique is different from the known proofs for the p − ∞ case as these proofs do not generalize to p ≠ ∞. For k − 1 and p − ∞, the μ problem is known to be NP-hard. We provide an alternative proof of this result. For k = 1 and p finite the issue of NP-hardness remains unresolved. When every block has size 1, and p − 2 we outline some potential difficulties in computing μ.

A lattice structure for perfect reconstruction linear time varying filter banks with all pass analysis banks

Abstract: We consider a multi-input, multi-output lattice realization for linear time-varying analysis banks which are all pass. Such a realization was given by Vaidyanathan and Mitra (1985) for linear time invariance (LTI) systems; and under certain conditions generalizes to the linear time varying (LTV) case. Moreover, our implementation is simpler than the one presented by Vaidyanathan et al. Finally, we describe the anticausal inverse of a lattice realization which is used in the synthesis bank.

Robust stability analysis for time-delay systems using the integral quadratic constraint approach

Abstract: Given a time-delay system, we are interested in finding new robust stability conditions for the system. We apply the integral quadratic constraint approach to obtain two results which allow us to test the robust stability using the linear matrix inequality technique. Both results give an estimate of the maximum time-delay which preserves robust stability. The first result is simpler to apply while the second one gives a less conservative robust stability condition.

Dyadic factorization of all pass IIR linear time varying analysis banks in multirate signal processing

Abstract: We consider a factorization scheme for linear time varying (LTV) IIR all pass systems to be used specifically in the analysis bank of multirate subband coders. The factorization scheme is based on a certain base dyadic structure. Such LTV analysis banks are required to be square systems. It is known that linear time invariant (LTI) square all pass systems admit such dyadic factorizations and that a limited class of FIR LTV all pass square systems have a specialized dyadic factorization. We extend these results to all pass IIR LTV square systems that have uniformly completely observable and uniformly completely controllable realizations.