Let S = {x ∈ R n : g 1 (x) ≥ 0, · · · , gm(x) ≥ 0} be a semialgebraic set defined by multivariate polynomials g i (x). Assume S is compact, convex and has nonempty interior. Let S i = {x ∈ R n : g i (x) ≥ 0} and ∂S i = {x ∈ R n : g i (x) = 0} be its boundary. This paper, as does the subject of semidefinite programming (SDP), concerns Linear Matrix Inequalities (LMIs). The set S is said to have ...

Let S = {x ∈ R n : g 1 (x) ≥ 0, · · · , gm(x) ≥ 0} be a semialgebraic set defined by multivariate polynomials g i (x). does the subject of semidefinite programming (SDP), concerns Linear Matrix Inequalities (LMIs). The set S is said to have an LMI representation if it equals the set of solutions to some LMI and it is known that some convex S may not be LMI representable [7]. A question arising ...

1 This work (Sycadi project) was supported by Region Rhones-Alpes, France Abstract: In this paper, a linear matrix equality (LMI) based H∞ filtering formulation is presented for fault detection and isolation (FDI) problems of linear time-invariant descriptor systems. The fixed-order H∞ FDI filter design is characterized in terms of definite LMIs with no equality constraint, which are done recen...

This paper deals with the design of resilient Cooperative Adaptive Cruise Control (CACC) for homogeneous vehicle platoons in which communication is vulnerable to Denial-of-Service (DOS) attacks. We consider DOS attacks as consecutive packet dropouts. present a controller tuning procedure based on linear matrix inequalities (LMI) that maximizes resiliency attacks, while guaranteeing performance ...

This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some...

This paper focuses on the chaos control problem of the unified chaotic systems with structured uncertainties. Applying Schur-complement and some matrix manipulation techniques, the controlled uncertain unified chaotic system is then transformed into the linear matrix inequality LMI form. Based on Lyapunov stability theory and linear matrix inequality LMI formulation, a simple linear feedback co...

* School of Mathematics and Statistics, Anyang Normal University 436 Xian’ge Road, 455000, Anyang, China ([email protected]) Abstract In this paper we consider the finite-time control problem for a class of networked systems with state delay and communication delay. The main result provided is a sufficient condition for the design of a state feedback controller which makes the closed loop system...

One of the most relevant problems for control engineers is the so-called “mixed H2/H∞”. To solve it, different convexifying strategies became popular in the later 1990s, mainly based on Linear Matrix Inequalities (LMIs). On the other hand, genetic algorithms have also been applied for H2/H∞ synthesis. Indeed, several authors agree that they are able to find good solutions to this important cont...

This paper presents a linear matrix inequalities (LMI) approach to robust tunable control. This controller design technique provides a new on-line tuning strategy for industrial process control systems. The tuning strategy is based on the performance robustness bounds of the system and knowledge of the plant uncertainty’s weighting function, which may change with time. The internal model contro...

We consider balanced flows in a natural gas transmission network and discuss computationally hard problems such as establishing if solution of the underlying nonlinear gas flow equations exists, if it is unique, and finding the solution. Particular topologies, e.g. trees, are known to be easy to solve based on a variational description of the gas flow equations, but these approaches do not gene...