On strong stabilization for linear time-varying systems

This paper deals with the strong stabilization problem for linear time-varying systems and gives a sufficient condition, in terms of the coprime factors, for the existence of strong stabilizers for such a system.     

Factorization and the Nehari theorem in time-varying systems

The Nehari Theorem and related results on operator interpolation play an important role in modern system theory. These results are embedded in a function-theoretic conceptual framework and therefore restricted to LTI systems. We give a state space oriented extension of the Nehari Theorem to a time-varying system-theoretic setting. In that setting the theorem addresses the issue of measuring the distance between a noncausal bounded I/O operator and the family of causal I/O operators in stable linear systems. The analysis is based on the recent time-domain LQ optimization approach to robust control. The discussion includes a geometrical analysis of stable and antistable invariant subspaces, a short study of certain types of co-prime factorizations of I/O operators in time-varying systems, and a parametrization of all suboptimal solutions.The research was supported in part by the National Science Foundation under Grant ECS 9108927 and by the U.S. Army Research Office under Contract DAALO3 92 G 0015.The research was supported by NSERC, Canada.     

A general time-varying estimation and control problem

This paper solves two problems raised in [HSK]. The first is a uniform norm time-varying linear estimation problem and the second is a general time-varying linear control problem.     

A small gain theorem for systems with non-causal subsystems

Small gain theorems are used to verify the stability of a feedback interconnection of causal stable systems. In this work, we extend the small gain condition to test the stability of a feedback interconnection of two stable systems at least one of which is non-causal. This result may find application in the robust controller design for time-delay systems.     

Lyapunov functions for time-varying systems satisfying generalized conditions of Matrosov theorem

The classical Matrosov theorem concludes uniform asymptotic stability of time-varying systems via a weak Lyapunov function (positive definite, decrescent, with negative semi-definite derivative along solutions) and another auxiliary function with derivative that is strictly nonzero where the derivative of the Lyapunov function is zero (Mastrosov in J Appl Math Mech 26:1337–1353, 1962). Recently, several generalizations of the classical Matrosov theorem have been reported in Loria et al. (IEEE Trans Autom Control 50:183–198, 2005). None of these results provides a construction of a strong Lyapunov function (positive definite, decrescent, with negative definite derivative along solutions) which is a very useful analysis and controller design tool for nonlinear systems. Inspired by generalized Matrosov conditions in Loria et al. (IEEE Trans Autom Control 50:183–198, 2005), we provide a construction of a strong Lyapunov function via an appropriate weak Lyapunov function and a set of Lyapunov-like functions whose derivatives along solutions of the system satisfy inequalities that have a particular triangular structure. Our results will be very useful in a range of situations where strong Lyapunov functions are needed, such as robustness analysis and Lyapunov function-based controller redesign. We illustrate our results by constructing a strong Lyapunov function for a simple Euler-Lagrange system controlled by an adaptive controller and use this result to determine an ISS controller.     

A robust control approach to stabilization of networked control systems with time-varying delays

The stabilization problem is studied for networked control systems (NCSs) with time-varying delay that may be larger than one sampling period. By considering state feedback controllers, the closed-loop NCS is described as a switched delay system, which is then represented as an interconnected feedback system. A sufficient BIBO stability condition is derived for the closed-loop NCS by using the small gain theorem and the average dwell time technique. Design procedures for the BIBO stabilizing controllers are also presented. An example is given to demonstrate the effectiveness of the proposed method.     

Cluster formation in a time-varying multi-agent system

We introduce time-varying parameters in a multi-agent clustering model and we derive necessary and sufficient conditions for the occurrence of clustering behavior with respect to a given cluster structure. For periodically varying parameters the clustering conditions may be formulated in a similar way as for the time-invariant model. The results require the individual weights assigned to the agents to be constant. For time-varying weights we illustrate with an example that the obtained results can no longer be applied.     

A sufficient condition for asymptotic stability for a class of time-varying parameterized systems

We derive sufficient conditions for local asymptotic stability for a class of parameterized time-varying systems, whose dynamics are in general unbounded in time. Our main result generalizes a well known limiting-dynamics based approach due to Peuteman and Aeyels (1999) in [9] for fast time-varying systems whose dynamics are bounded in time. Its proof is based on a new result providing a Lyapunov characterization for exponential stability.     

A time-varying extremum-seeking control approach for discrete-time systems

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying discrete-time estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signals on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.     

Robust observability for a class of time-varying discrete-time uncertain systems

This paper introduces a concept of robust observability for a class of uncertain discrete-time systems. This notion is an extension of the standard notion of observability for discrete-time, linear time-varying systems. The uncertainty and noise are modelled deterministically via a sum quadratic constraint. A necessary and sufficient condition for robust observability is presented in terms of existence of a suitable solution to a Riccati difference equation. The set of possible initial states given noisy measurements over a finite number of sampling periods is shown to be an ellipsoid.     

A new procedure for time-varying linearization up to output injection

New necessary and sufficient conditions for time-varying linearization up to output injection (TVLOI) are presented. They yield a straightforward TVLOI procedure.     

The subspace Nevanlinna interpolation problem and the most powerful unfalsified model

A generalization of the tangential Nevanlinna interpolation problem will be studied from a behavioral point of view. Necessary and sufficient conditions for its solvability and a characterization of all its solutions are derived. These results are obtained by associating to the interpolation data a behavior that enjoys a special structure.     

The time-varying gap and coprime factor perturbations

The connection between the time-varying gap metric and two-block problems is utilized to obtain criteria for robust stabilization of linear, discretetime, time-varying systems. In particular we give a formula for the optimal minimal angle for a stabilizable linear time-varying system and show that it has a maximally stabilizing controller.     

On a large-gain theorem

The aim of this paper is to give a general quantitative requirement which the loop gain must satisfy in order to stabilize a given unstable (possibly nonlinear and time-varying) plant, namely that the gain must exceed one.     

A Java-based intelligent advisor for selecting a context-appropriate spatial interpolation algorithm

The choice of an appropriate interpolation technique is an imposing task. There are many techniques to choose from depending on the characteristics of the phenomenon, the purpose of the study and also the expertise of the user. This paper describes the implementation and architecture of a Java-based intelligent advisor to assist a generic user, ranging from the casual to the specialist, in selecting the interpolator most appropriate for a given task and data set. The software integrates procedural knowledge from disparate sources through an expert system shell, and uses multiple sensory channels to present and abstract contextual knowledge from the user regarding both the data and the task at hand. The system has been tested for use in a meteorological domain in the first instance. The interpolation methods currently assessed by the system are multiple forms of kriging, thin plate smoothing splines, inverse-distance weighting and trend surface/polynomial analysis.     

Links between asymptotic controllability and persistence of excitation for a class of time-varying systems

For a class of nonlinear time-varying parameterized systems we prove that persistence of excitation implies global asymptotic controllability to the equilibrium with respect to a set of parameters. The result is used to derive sufficient conditions for global asymptotic controllability for composite systems.     

On polytopic inclusions as a modeling framework for systems with time-varying delays

One of the important issues in networked control systems is the appropriate handling of the nonlinearities arising from uncertain time-varying delays. In this paper, using the Cayley-Hamilton theorem, we develop a novel method for creating discrete-time models of linear systems with time-varying input delays based on polytopic inclusions. The proposed method is compared with existing approaches in terms of conservativeness, scalability and suitability for controller synthesis.     

A new Lyapunov function for stability of time-varying nonlinear perturbed systems

In this paper, global and local uniform asymptotic stability of perturbed dynamical systems is studied by using Lyapunov techniques. The restriction about the perturbed term is that the perturbation is bounded by an integrable function under the assumption that the nominal system is globally uniformly asymptotically stable. We use a new Lyapunov function to obtain a global uniform asymptotical stability of some perturbed systems.