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Systems with Action of Parameters
Systems with Single Variable Control
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adj(s adjoint matrix algebra antistable antistable manifolds approximate linearization Assertion asymptotically stable basic called centre manifold chaos chaotic attractor chaotic behaviour Chapter characteristic polynomial complex frequency domain components computation condition continuous-time control systems corresponding criterion defined Definition denote det(s diffeomorphism discrete-time dynamical system eigenstructure eigenvalues equilibrium point equivalent example exists feedback frequency characteristic gain global homoclinic orbit hyperbolic input integration invariant set left eigenvectors Let us consider limit cycle linear system loops Lorenz Lyapunov exponents Mason graph matrix F matrix group multiplicity nonhyperbolic nonlinear systems numerical Nyquist observation obtain open control circuit output parameters paths poles prescribed PROOF reachable real axis regulator REMARKS right eigenvectors robustness root locus s-plane semisimple semistable shown in Figure smooth solution stability boundary stabilizable stable and antistable stable manifold subspace symmetry symplectic symplectic matrix synthesis system x Theorem trajectories transfer transformation unstable vector zero