Pair Of Linear Matrix Inequalities Research Articles

An Alternative Algorithm to the D-K Iterations for Robust Control Design

This letter presents a new algorithm for designing robust output-feedback controllers in the presence of structured uncertainty. The proposed approach is an alternative to the popular D-K Iterations, consisting of a pair of LMIs (Linear Matrix Inequalities) and an associated iterative algorithm. The new algorithm is illustrated by examples and its performance is compared with the D-K iterations by solving instances of the COMPleib benchmark library.

A Linear Fractional Transform (LFT) Based Model for Interconnect Uncertainty

As we scale toward nanometer technologies, the increase in interconnect parameter variations will bring significant performance variability. New design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new performance models which accurately capture the manufacturing realities. In this paper, we present a Linear Fractional Transform (LFT) based model for interconnect parametric uncertainty. The new model formulates the interconnect parametric uncertainty as a repeated scalar uncertainty structure. With the help of generalized Balanced Truncation Realization (BTR) and Linear Matrix Inequalities (LMI's), the porposed model reduces the order of the original interconnect network while preserves the stability. The LFT based new model even guarantees passivity if the BTR reduction is based on solutions to a pair of Linear Matrix Inequalities (LMI's) generated from Lur'e equations. In case of large number of uncertain parameters, the new model may be applied successively: the uncertain parameters are partitioned into groups, and with regard to each group, LFT based model is applied in turns.

An Exact Stability Analysis Test for Single-Parameter Polynomially-Dependent Linear Systems

We provide a condition for testing the stability of a single-parameter, polynomially-dependent linear system of polynomial degree N of the form x/sup /spl dot// = A(/spl rho/)x, A(/spl rho/) = /spl Sigma/ /sub i=0//sup N//spl rho//sup i/A/sub i/ over a compact interval. The test is nonconservative and can be cast as a convex feasibility problem in terms of a pair of linear matrix inequalities (LMIs).

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

Abstract In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2, H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

A necessary and sufficient minimality condition for uncertain systems

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFTs) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well as Kalman-like decomposition structures. A related minimality condition, the converse of the reducibility condition, may then be inferred from these results and the equivalence class of all minimal LFT realizations defined. These results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems. Subsequent results, such as the definition of and rank tests on structured controllability and observability matrices are also given. The minimality results described are applicable to multidimensional system realizations as well as to uncertain systems; connections to formal powers series representations also exist.

Low-order control design for LMI problems using alternating projection methods

Computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities (LMIs). In particular, we concentrate on the stabilization and the suboptimal H ∞ output feedback control design problems. These problems can be described by a pair of LMIs and an additional coupling condition. This coupling condition is convex for the full-order control design problem, but convexity is lost for the control problem of order strictly less than the plant order. We formulate these problems as feasibility problems with matrix constraint sets of simple geometry, and we utilize this geometry to obtain analytical expressions for the orthogonal projection operators onto these sets. Full-order and low-order controllers are designed using alternating projection methods. For the full-order controller case, global convergence of the alternating projection methods to a feasible solution is guaranteed. However, for the low-order control case, only local convergence is guaranteed. An example is provided to illustrate the use of these methods for the full-order and the low-order controller design.

Model reduction of multidimensional and uncertain systems

Model reduction methods are presented for systems represented by a linear fractional transformation on a repeated scalar uncertainty structure. These methods involve a complete generalization of balanced realizations, balanced Gramians, and balanced truncation model reduction with guaranteed error bounds, based on solutions to a pair of linear matrix inequalities which generalize Lyapunov equations. The resulting reduction methods immediately apply to uncertainty simplification and state order reduction in the case of uncertain systems but also may be interpreted as state order reduction for multidimensional systems.