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Structured and Simultaneous Lyapunov Functions for System Stability Problems
Structured Simultaneous Lyapunov Functions System Stability Problems
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2015/7/13
It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of dx/dt...
Computation of the Maximum H_infinity-norm of Parameter-Dependent Linear Systems by a Branch and Bound Algorithm
Computation Maximum H_infinity-norm Parameter-Dependent Linear Systems Bound Algorithm
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2015/7/13
For linear systems that contain unspecified parameters that lie in given intervals, we present a branch and bound algorithm for computing the maximum H_infinity-norm over the set of uncertain paramete...
Branch and Bound Algorithm for Computing the Minimum Stability Degree of Parameter-Dependent Linear Systems
Branch Bound Algorithm Computing Minimum Stability Degree Parameter-Dependent Linear Systems
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2015/7/13
We consider linear systems with unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems ca...
Computing Bounds for the Structured Singular Value via an Interior Point Algorithm
Computing Bounds Structured Singular Value Interior Point Algorithm
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2015/7/13
We describe an interior point algorithm for computing the upper bound for the structured singular value described in the paper by Fan, Tits and Doyle, IEEE Trans AC, Jan. 1991. We demonstrate the perf...
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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2015/7/13
Gives some vague ideas about useful control design tools that might be based on LMI algorithms.