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INTRODUCTION TO SYSTEMS
STABILITY OF SYSTEMS
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assumed asymptotically stable autocorrelation function axes blocks boundary calculate coefficients column completely randomized design components Consider constant contraction mapping convergent critical point defined degrees of freedom density function determined displacement effect eigenvalues eigenvectors equilibrium point error Euler-Lagrange equations example experiment factor finite element follows fundamental matrix given gives Hence inner product space input interaction Liapunov function linear system load meter method metric space minimise negative nodal forces nodes norm notation Note observations obtain output phase plane phase plane portrait positive definite possible probability density function problem random process random variable replications Rx(t sample function scalar second-order tensor sequence Show shown in Figure solution solve specified stationary strain stress tensor sum of squares Suppose symmetric system x Table temperature Theorem trajectory transformation unstable variation vector verify zero