Solvability Of Linear Matrix Inequalities Research Articles

H 2 ∕ H ∞ Robust Static Output Feedback Control Design via Mixed Genetic Algorithm and Linear Matrix Inequalities

This paper is concerned with the synthesis of a mixed H2∕H∞ robust static output feedback with a bounded control bandwidth for continuous-time uncertainty systems. To this end, genetic algorithms and a linear matrix inequality solver are employed to regulate the static output feedback gains and to examine the Lyapunov stability conditions, respectively. The fitness function of this paper, which is called a hierarchical fitness function structure (HFFS), is able to deal with the stability conditions and the performance constraints in turn. This HFFS not only saves computing time but can also identify the infeasible stability condition. Designers can use the proposed idea to deal with many complex output feedback control problems. It also limits elaborate mathematical derivations and extra constraints.

H∞ Control of Descriptor Systems: An Application from Binary Distillation Control

In this paper the H∞ control problem for descriptor systems is considered. This problem can efficiently be solved by specialization of a recent solution of the general quadratic performance control problem to the H∞ case. The solution is given in terms of strict linear matrix inequality (LMI) conditions. Contrary to previous solutions of the descriptor H∞ control problem, these synthesis conditions can easily be evaluated by standard LMI solvers. The presented synthesis result is applied to a S/KS H∞ control problem from binary distillation control. The process model of the underlying separation process is given by means of a phenomenological descriptor model which describes the movement of concentration profiles in rectifying and stripping section of the distillation column.

Multicriterion optimized QMF bank design

The quadrature mirror filter (QMF) bank with multicriterion constraints such as minimal aliasing and/or minimal error coding is among the most important problems in filterbank design, for solving which linear algebra-based methods are still heuristic and do not always work, especially for large filter length. It is shown in this paper that this problem can be reduced either to convex linear matrix inequality (LMI) optimization (when filters are of nonlinear phase) or to semi-infinite linear (SIP) programming (when filters are of linear phase), which can be very efficiently solved either by the standard LMI solvers or our previously developed SIP solver. The proposed computationally tractable optimization formulations are confirmed by several simulations.

Editorial: Linear matrix inequalities

Linear matrix inequalities (LMIs) have emerged as a powerful tool for numerically solving control problems that are difficult or impossible to solve analytically. The idea is to express a given problem as an optimisation problem with linear objective and semidefinite constraints, where the constraints involve symmetric matrices that are affine in the decision variables. Once a problem has been expressed in this form, efficient LMI solvers can be used to obtain a numerical solution. This Special Section on LMIs for application in control engineering collects a number of recent results in various fields such as linear parameter-varying (LPV) systems, predictive control, sliding mode control, and applications such as control of networked or interconnected systems and robust design of power system stabilisers

Reliable Robust Preview Tracking Control Against Actuator Faults

ABSTRACTIn this paper we provide a solution to the reliable robust preview tracking problem against actuator faults for discrete LTI systems with polytopic uncertainties. This solution is in terms of the solvability of linear matrix inequalities (LMIs). The method is based on multi‐objective optimization and LQ tracking performance indices. To avoid the conservativeness problem associated with using a common LMI solution for the normal case and the fault cases, different LMI solutions are used in the proposed method. Two iterative algorithms are proposed and compared. Numerical examples are used to show the effectiveness of the algorithms.

Delay-independent circle criterion and popov criterion

In the present paper are studied delay-independent versions of circle criterion and Popov criterion, for some nonlinear delay systenls with sector-bounded nonlinearities. Necessary and sufficient conditions are obtained in terms of solvability of linear matrix inequalities. This constitutes an analogue to the famous results, valid for nonlinear delay-free systems

An efficient solution to multi-objective control problems with LMI objectives

We revisit a technique for solving multi-objective control problems through affinely parameterizing the closed-loop system with the Youla parameterization and confining the search of the Youla parameter to finite-dimensional subspaces. It is pretty well-known how to solve such problems if the closed-loop specifications are formulated in terms of the solvability of linear matrix inequalities. However, all approaches proposed so far suffer from a substantial inflation of size of the resulting optimization problems if improving the approximation accuracy. On the basis of a novel state-space approach to solving static output feedback control problems by convex optimization for a specific class of plants, we reveal how the growth of the size of the optimization problems can be considerably reduced to arrive at more efficient algorithms. As an additional ingredient we discuss how to use the so-called mixed controller as a starting point for a genuine multi-objective design in order to improve the algorithms.