This paper considers the L2-L∞ model reduction problems for polytopic system with time-varying delay. In terms of the solution of linear matrix inequalities (LMIs) and inverse constraints, sufficient conditions are presented to construct the reduced order models such that the L2-L∞ gain of the error system between the full order model and the reduced order one is less than a given scalar.

Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guarantee...

This paper is concerned with the decentralized stabilization problem for a class of uncertain large-scale systems with Markovian jump parameters. The controllers use local subsystem states and neighboring mode information to generate local control inputs. A sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers. A numerical exam...

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here we give new results on the relatively open problem of the design of physically based control ...

The solvability conditions for positive real and *-norm controller synthesis problems are expressed in terms of linear matrix inequalities that include the compensator gains implicitly. A variety of issues, including explicit expressions for the solutions, the issue of strictly proper vs proper controllers and relaxing full rank assumptions on the penalty matrices can be discussed. Extension to...

This note concerns the optimal H∞ unbiased filtering problem for linear descriptor systems. It unifies the design of reduced-order, minimal-order and full-order filters for continuous and discrete-time systems. Necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of linear matrix inequalities (LMIs). The parametrization of all H∞ unbiased filters...

An Inexact Bundle Method for Solving Large Structured Linear Matrix Inequalities

This paper is concerned with the problem of H∞ filter design for linear continuous-time state-delayed systems with finite frequency specifications. The developed approaches in the paper are to design a filter guaranteeing an H∞ performance bound in a finite frequency range for delayed systems. To reduce conservatism, delay-partitioning idea is exploited to derive a new finite frequency bounded ...

We consider the problem of reducing a model in a way that preserves a partition of the system states. This is motivated, for instance, in situations where state variables are associated with the topology of a networked system. In earlier work we proposed an LMI method based on block-structured generalized controllability and observability gramians; to make such strategy feasible, coprime factor...

In this paper, we consider the distributed robust filtering problem, where estimator design is based on a set of coupled linear matrix inequalities (LMIs). We separate the problem and show that the method of multipliers can be applied to obtain a solution efficiently and in a decentralized fashion, i.e. all local estimators can compute their filter gains locally, with communications restricted ...