Robust Stability Bounds on Structured Time-Varying Independent Perturbations for Linear State-Space Models

Given a stable linear time-invariant dynamical system x·= Ax, it is shown that there exists a related stable family of dynamical systems x·=A(k)x. The Lyapunov stability criterion remains valid for all linear operators A(k)=DkA of this family.

We discuss the stabilization of large scale linear time invariant dynamical systems via feedback. An overview of efficient schemes based on the discrete Riccati difference equation are presented. In particular, results are given for a Newton-like approach to the problem.

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.

This paper presents a sufficient condition that establishes closed loop stability for linear time invariant dynamical systems with transfer functions that are analytic in the open right half complex plane. The condition is suitable for analyzing a large class of highly complex, possibly interconnected, systems. The result is based on bounding Nyquist curves by using frequency dependent half planes. It provides (usually non-trivial) robustness guarantees for the provably stable systems and generalizes to the multidimensional case using matrix field of values. Concrete examples illustrate the applications of the condition. From our condition, it is easy to derive a relaxed version of the classical result that the interconnection of a positive real and strictly positive real linear system under feedback is closed loop stable.

This paper considers the problem of robust stabilization of non-minimum phase linear time-invariant single-input single-output uncertain systems. Under certain assumptions, it is shown that non-minimum phase LTI uncertain systems with known order and known and invariant relative degree can be controlled to achieve robust stability by using a linear periodic output feedback controller. The authors' result generalizes similar results for LTI minimum phase uncertain systems. >

Consistent estimation of real NMP zeros in stable LTI systems of arbitrary complexity

We study the decentralized stabilization problem of linear time-invariant large scale interconnected systems with delays. We obtain a sufficient decentralization condition for unforced systems and use this analysis result to obtain a decentralized state-feedback controller using standard H/sub /spl infin// control theory. We also obtain a decentralized observer for the interconnected system.

On Reconfigurability

This paper deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals. We propose a new controller parameter optimization approach, which can be carried out experimentally without knowledge of the plant model or the order of the system. The approach has the advantages that controllers can be tuned by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

The stability robustness of linear time-variant systems with both time-varying structured and unstructured perturbations is investigated by using the Lyapunov approach and some essential properties of matrix measures. Some new sufficient conditions are proposed for ensuring the linear time-variant systems with both time-varying structured and unstructured perturbations to be uniformly asymptotically stable. For the case that the linear time-variant system only subjects to time-varying structured perturbations, by mathematical analysis, the presented sufficient conditions are proved to be less conservative than the existing ones reported in the literature. The result only for structured independent time-varying perturbations case is also extended to the stability analysis of time-variant interval systems.

ROBUST STABILITY ANALYSIS FOR STRUCTURED UNCERTAINTIES WITH BOUNDED VARIATION RATES

This paper deals with the question of the existence of weak and strong common
\nquadratic Lyapunov functions (CQLFs) for stable discrete-time linear timeinvariant
\n(LTI) systems. The main result of the paper provides a simple characterisation
\nof pairs of such systems for which a weak CQLF of a given form exists
\nbut for which no strong CQLF exists. An application of this result to second
\norder discrete-time LTI systems is presented.

The authors establish a generalized frequency-domain criterion for checking families of polynomials for root confinement in open subsets of the complex plane. The authors show how this criterion reduces to checking certain curves in the complex plane for zero confinement. Moreover, in some special cases, it further reduces to some complex functions with pointwise phase differences that are always less than pi in magnitude. Most of the currently available results on the robust stability of linear systems with parametric uncertainties can be viewed within the unifying frequency-domain framework presented. The framework encapsulates not just finite-dimensional systems, but any linear-time-invariant (LTI) system that can be characterized by transfer functions of a single variable. It also covers robust stability of LTI systems under passive feedback. >

The approximation of linear time-invariant (LTI) systems by sampling series is a central task of signal processing. For the Paley-Wiener space PW1 π of bandlimited signals with absolutely integrable Fourier transform, it is known that there exist signals and stable LTI systems such that the canonical approximation process diverges. In this paper we analyze the structure of the sets of signals and systems creating divergence and show that both sets are jointly spaceable, i.e., contain subsets such that every linear combination of signals and systems from these subsets, which is not the zero element, leads to divergence. In signal processing applications the linear structure of the involved signal spaces is essential. Here, we show that the same linear structure also holds for the sets of signals and systems creating divergence.

This paper is concerned with the nonlinear static state feedback stabilization of time-invariant linear multivariable continuous-time systems with friction driven backlash in the control inputs. A time-invariant static nonlinear state feedback compensator is proposed, easily obtainable solving an algebraic Riccati equation. The global asymptotic stability of the resulting closed-loop nonlinear system is proved using the Lyapunov's direct method and the La Salle's invariance principle. A simulation study shows that the proposed nonlinear state feedback compensator achieves an overall stabilization performance significantly better than the known backlash inverse compensator.