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Recent results have shown that several H_2 and H_2-related problems can be formulated as convex programs with a finite number of variables. We present an interior point algorithm for the solution of t...
On Maximizing a Robustness Measure for Structured Nonlinear Perturbations
Maximizing Robustness Measure Structured Nonlinear Perturbations
2015/7/13
In this paper, we propose a robustness measure for LTI systems with causal, nonlinear diagonal perturbations with finite L_2-gain. We propose an algorithm to reliably compute this quantity. We show ho...
Design of stabilizing state feedback for delay systems via convex optimization
stabilizing state feedback delay systems convex optimization
2015/7/13
For linear systems with delays, we define a new class of Lyapunov-like functionals that may be used to prove stability. We also show how we may design a stabilizing (delayed) state feedback for delay ...
Global Optimization in Control System Analysis and Design
Global Optimization Control System Analysis Design
2015/7/13
We present branch and bound algorithms for the computation of several important quantities (best- and worst-case norms and best- and worst-case state decay rates) that arise in the analysis and design...
On Computing the Worst-Case Peak Gain of Linear Systems
SISO discrete-time LTI systems computation of `1-gain discrete-time systems with diagonal perturbations
2015/7/13
Based on the bounds in the paper by Boyd and Doyle (Comparison of peak and RMS gains for discrete-time systems, Systems and Control Letters, 9:1-6), we present simple upper and lower bounds for the el...
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
polynomial-time algorithm determining quadratic Lyapunov functions nonlinear systems
2015/7/13
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
Control system analysis and synthesis via linear matrix inequalities
Control system analysis synthesis linear matrix inequalities
2015/7/13
A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are “analytical sol...
Solving interpolation problems via generalized eigenvalue minimization
Solving interpolation problems generalized eigenvalue minimization
2015/7/13
A number of problems in the analysis and design of control systems may be reformulated as the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices which depend affi...
Closed-Loop Convex Formulation of Classical and Singular Value Loop Shaping
Closed-Loop Convex Formulation Classical Singular Value Loop Shaping
2015/7/13
We show that control system design via classical loop shaping and singular value loop shaping can be formulated as a closed-loop convex problem. Consequently, loop shaping problems can be solved by ef...
Method of centers for minimizing generalized eigenvalues
quasiconvex nondifferentiable optimization generalized eigenvalue
2015/7/13
We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear spe...
Robust Control Tools:Graphical User-Interfaces and LMI Algorithms
Robust Control Tools Graphical User-Interfaces LMI Algorithms
2015/7/13
Gives some vague ideas about useful control design tools that might be based on LMI algorithms.
Existence and Uniqueness of Optimal Matrix Scalings
diagonal similarity scalings scaled singular value minimization irreducible matrices
2015/7/13
We show that the set of diagonal similarity scalings that minimize the scaled singular value of a matrix is nonempty and bounded if and only if the matrix that is being scaled is irreducible. For an i...
Efficient Convex Optimization for Engineering Design
Optimization numerical methods linear programming robust control convex programming interior-point methods
2015/7/13
Many problems in engineering analysis and design can be cast as convex optimization problems, often nonlinear and nondifferentiable. We give a high-level description of recently developed interior-poi...
Robust Control Tools:Graphical User-Interfaces and LMI Algorithms
Robust Control Tools Graphical User-Interfaces LMI Algorithms
2015/7/13
Gives some vague ideas about useful control design tools that might be based on LMI algorithms.
Existence and Uniqueness of Optimal Matrix Scalings
diagonal similarity scalings scaled singular value minimization irreducible matrices
2015/7/13
We show that the set of diagonal similarity scalings that minimize the scaled singular value of a matrix is nonempty and bounded if and only if the matrix that is being scaled is irreducible. For an i...