## Automated design of control systems |

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absolute minimum addition admissible assumed Assumption asymptotically stable automated design canonical equations characteristic polynomial closed-loop system coefﬁcient matrices computational methods computer program conjugate gradient method control system convergence convex functions convex set corresponding deﬁned denoted depicted in Figure derived design problems deterministic differential equations difﬁculties direction vector eigenvalues equality constraints equivalent example exists feedback control feedback gains ﬁrst formulation functional f hence hessian holds inequality constraints introduced iteration Lagrange multiplier Lagrangian Laplace transform Lemma linear optimal control method of successive min-max method minimization Moreover necessary condition Newton-Raphson method nonsingular open-loop optimal forcing functions optimal gain control parameter optimization performance functional performance integral positive deﬁnite positive semi-deﬁnite properties quadratic function relative minimum Repeat Problem respect satisﬁed selection signiﬁcance solving stationarity stochastic strictly convex successive approximations successive substitutions sufﬁcient conditions Suppose f Table tangent space Td(s Theorem transfer function twice continuously differentiable variables yields