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A.M. Reinhorn A.S. Cakmak A.S. Veletsos active bracing system active mass damper Analysis aseismic hybrid control base isolation system C.S. Lee cc xi Center for Earthquake columns control algorithms control of nonlinear controlled structure damping ratio denoted dependent performance index designated diagonal matrix Earthquake Engineering Research earthquake episode energy concept equation of motion Experimental Feedback floor G.C. Lee gain matrix given by Eq Ground Motions guarantee the stability Hwang hybrid control system hysteretic structural systems instantaneous optimal control K.C. Chang linear algebraic linear structures Lyapunov direct method Lyapunov function Lyapunov method M.C. Constantinou matrix Q maximum response quantities Model negative semidefinite nonlinear or hysteretic NTIS see address observed from Table positive semidefinite matrix possible choices Q matrix quantities are shown Reinforced Concrete report is available Riccati equation Riccati matrix Riccati-type matrix equation Seismic Analysis Shinozuka shown in Fig stiffness Structural Control system matrix T.T. Soong Table 4-n Viscoelastic weighting matrix