Facilities such as buildings, highways, railways, bridges, dams and pipelines often are built on natural slopes where the risk of landslides is not low. The vulnerability of these facilities to slowmoving slides has sometimes been underestimated, although the velocity of some classes of slow slides is uncontrollable. More than 50 cases of slow slides were compiled from the literature for this study. Some statistics about the movement trigger(s), the methods used to measure displacement, the material forming the rupture surface and the type of the vulnerable facilities are presented. It is shown that the expected degree of damage to urban settlements, highways, bridges and dams can be related to the slide velocity or accumulating displacement. Buildings and residential houses may tolerate higher slide velocities and total displacements than other facilities before experiencing serious damage. Movements as low as 100mm may severely damage bridges, but such low rates may cause only moderate damage to urban communities. The relationship between movement and the expected extent of damage should be useful to geotechnical engineers who deal with different classes of slow slides and will help in the choice of appropriate mitigation measures based on preliminary estimates of movement rates.

The stability of two-dimensional, linear, discrete systems is examined using the 2-D matrix Lyapunov equation. While the existence of a positive definite solution pair to the 2-D Lyapunov equation is sufficient for stability, the paper proves that such existence is not necessary for stability, disproving a long-standing conjecture.

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A, B. K, and L , K 2 can be computed as K 2 = [ o 0 -21 K = [ -l 0 0 -21. VI. CONCLUSIONSA decomposition of a large control system into a block triangular structure of input reachable subsystems can be useful in several ways. First. the stabilization problem of the overall system is reduced to stabilization of a number of smaller problems associated with the subsystems. Second. the special structure of the subsystems allows for a "pieceby-piece" computation of the feedback gains providing an additional possibility for dimensionality reduction of the stabilization problem. Furthermore. once the block triangular structure is determined. the interconnections which are outside of the subsystems can be identified as interconnections which have no effect on stability of the overall closed-loop system. It should also be mentioned that the decomposition scheme, being independent of the nature of the equations (nonlinear. discrete, etc.). can be used for stabilization of wider classes of systems than presently considered, provided the obtained subsystems can be stabilized by known methods. REFERENCES [ I ] D D SllJak. "Stability of large-scale systems." in Prm. ? d l IF,4C Cong.. Paris. 121 A K KeLorklan. "Structural ahpectb of large d?namic sy>temh." In Prm O r h I F A C France. 191?. pp. C-32:I-I1 171 0. &goner and W. R Pcrkins. "Graph theor) in the anal\xr of large scale Cmr.. Bo>ton. MA. 1975. pp 19:1:1-7. composltc d>namlc b)stem>." in P r o . ltm Slnzp. Ctrcurr~ SI,? . Bodon. MA. 1975. [ I ] W Mayeda and N. Wax. "System StNCtUrc and rtahiht\." In P r o . IOrh Asrlontur [ 5 ] D b. SilJak. "On reachahilil> of dynamlc s>*temc." l n r . J . S u r Set.. w 1 8. pp [fi] E. 1. Datlsnn. "Connectahilit) and structural controllahilit! of componte syrlcmn." 171 D. D. SilJak. 'On pure structure of dynamic $yslemr." 3'ottlrneur Sriul.. T h e m . [ X ] F M Callicr. W S. Cham and C A. Dchoer. "Input-output stah~htr of Intercon-pp. 121-113 Con/. C m w o . Stsr Cmnpur .

A new algorithm for audio watermarking is proposed. The basic idea of the algorithm is to change the length of the intervals between salient points of the audio signal to embed data. We propose several novel ideas for practical implementations that can be used by other watermarking schemes as well. The algorithm is robust to common audio processing operations e.g. mp3 lossy compression, low pass filtering, and time-scale modification. The watermarked signal has very high perceptual quality and is indistinguishable from the original signal.