Robust stability and a criss-cross algorithm for pseudospectra
نویسنده
چکیده
A dynamical system ẋ = Ax is robustly stable when all eigenvalues of complex matrices within a given distance of the square matrix A lie in the left half-plane. The ‘pseudospectral abscissa’, which is the largest real part of such an eigenvalue, measures the robust stability of A. We present an algorithm for computing the pseudospectral abscissa, prove global and local quadratic convergence, and discuss numerical implementation. As with analogous methods for calculating H∞ norms, our algorithm depends on computing the eigenvalues of associated Hamiltonian matrices.
منابع مشابه
Criss-Cross Type Algorithms for Computing the Real Pseudospectral Abscissa
The real ε-pseudospectrum of a real matrix A consists of the eigenvalues of all real matrices that are ε-close in spectral norm to A. The real pseudospectral abscissa, which is the largest real part of these eigenvalues for a prescribed value ε, measures the structured robust stability of A w.r.t. real perturbations. In this report, we introduce a criss-cross type algorithm to compute the real ...
متن کاملStability Analysis and Robust PID Control of Cable Driven Robots Considering Elasticity in Cables
In this paper robust PID control of fully-constrained cable driven parallel manipulators with elastic cables is studied in detail. In dynamic analysis, it is assumed that the dominant dynamics of cable can be approximated by linear axial spring. To develop the idea of control for cable robots with elastic cables, a robust PID control for cable driven robots with ideal rigid cables is firstly de...
متن کاملRobust Fixed-order Gain-scheduling Autopilot Design using State-space Stability-Preserving Interpolation
In this paper, a robust autopilot is proposed using stable interpolation based on Youla parameterization. The most important condition of stable interpolation between local controllers is the preservation of stability so that each local controller can ensure stability for an open neighborhood around a nominal point. The proposed design used fixed-order robust controller with parameter-dependent...
متن کاملThe finite criss-cross method for hyperbolic programming
In this paper the nite criss-cross method is generalized to solve hyperbolic programming problems. Just as in the case of linear or quadratic programming the criss-cross method can be initialized with any, not necessarily feasible basic solution. Finiteness of the procedure is proved under the usual mild assumptions. Some small numerical examples illustrate the main features of the algorithm.
متن کاملNew variants of finite criss-cross pivot algorithms for linear programming
In this paper we generalize the so called rst in last out pivot rule and the most often selected variable pivot rule for the simplex method as proposed in Zhang to the criss cross pivot setting where neither the primal nor the dual feasibility is preserved The nite ness of the new criss cross pivot variants is proven
متن کامل