相关论文: Linear Matrix Inequality Representation of Sets
Linear matrix Inequalities (LMIs) have had a major impact on control but formulating a problem as an LMI is an art. Recently there is the beginnings of a theory of which problems are in fact expressible as LMIs. For optimization purposes it…
A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the solution set…
The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and…
There has recently been ample interest in the question of which sets can be represented by linear matrix inequalities (LMIs). A necessary condition is that the set is rigidly convex, and it has been conjectured that rigid convexity is also…
Linear matrix inequalities (LMIs) commonly appear in systems, stability, and control applications. Many analysis and synthesis problems in these areas can be solved as feasibility or optimization problems subject to LMI constraints.…
This note introduces a sufficient Linear Matrix Inequality (LMI) condition for the ultimate boundedness of a class of continuous-time dynamical systems with conic uncertain/nonlinear terms.
Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) in the coefficients. As an…
LMI (Linear Matrix Inequalities) regions is an important class of convex subsets of $\mathbb C$ arising in control theory. An LMI region $\mathfrak D$ is defined by its matrix-valued characteristic function $f_{\mathfrak D}(z) = {\mathbf L}…
We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer…
Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions of MICP problems. We establish several…
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…
We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…
Linear-Quadratic (LQ) problems that arise in systems and controls include the classical optimal control problems of the Linear Quadratic Regulator (LQR) in both its deterministic and stochastic forms, as well as $H^\infty$-analysis (the…
Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a…
The regression problem associated with finding a matrix approximation of the Koopman operator from data is considered. The regression problem is formulated as a convex optimization problem subject to linear matrix inequality (LMI)…
In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent…
The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however…
A set $S\subseteq \re^n$ is called to be {\it Semidefinite (SDP)} representable if $S$ equals the projection of a set in higher dimensional space which is describable by some Linear Matrix Inequality (LMI). The contributions of this paper…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…