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This paper presents a robust telerobotic system that consists of a real-time vision-based operator hand tracking system (client) and a slave robot (server) which are interconnected through a LAN. The tracking system: 1) monitors the operator hand motion and 2) determines its position and orientation which are used to control the slave robot. Two digital cameras are used to monitor a four-ball-based feature frame that is held by the operator hand. To determine the three-dimensional (3-D) position a tracking algorithm based on uncalibrated cameras with weak perspective projection model is used. This allows finding 3-D differential position and orientation of the operator hand. The features of the proposed system are: 1) a metric for color matching to discriminate the balls from their background; 2) a uniform and spiral search approach to speed up the detection; 3) tracking in the presence of partial occlusion; 4) consolidate detection by using shape and geometric matching; and 5) dynamic update of the reference colors. The operator can see the effects of the previous motion which enables making the necessary corrections through repetitive operator hand-eye interactions. Evaluation shows that the static and dynamic errors of the tracking algorithm are 0.1% and 0.6% for a centered workspace of [20.sup.3] [in.sup.3] that is 40-60 in away from the cameras. Running the tracking algorithm on two PCs in parallel allowed: 1) a parallel image grabbing delay of 60 ms; 2) a stereo matching delay of 50 ms; and 3) a global refresh rate of 9 Hz. Index Terms--Robotics, stereo vision, telerobotics, three-dimensional (3-D) tracking, 3-D vision.

In this note, we study the conservatism of structured singular value computation by a randomized algorithm. It is proved that, if the maximization problem [micro](M) = max p(M [DELTA]) is solved by generating polynomial number of random [DELTA] samples and then taking the maximum of the function at these sample points, for any fixed lower bound on the confidence level, conservatism of the resulting estimate grows faster than any polynomial function of the logarithm of the matrix size. This result holds for purely complex, mixed, and purely real cases with no repeated blocks. However, it is shown to be not true if the number of samples exceeds some exponential function for the purely complex version of the problem. Although the estimate obtained by polynomial number of samples can be used to find an exact robustness margin with a high confidence level, for all except for a small relative volume of the uncertainty set, it has high conservatism for the worst-case robustness analysis, no matter how small the confidence level lower bound may be. The results of this note imply that conservatism will be large for certain classes of matrices. However, this does not eliminate the possibility of existence of other classes of matrices for which the conservatism is small. Index Terms--Randomized methods, structured singular value.

In this paper, we investigate tracking properties of linear shift-invariant feedback control systems. We consider the standard unity feedback configuration, and use the energy of an error signal as a measure of tracking ability. Our main goal is to understand the fundamental limitation on tracking performance, which can arise due to the nonminimum phase zeros, unstable poles, and time delays in the plant, and which varies with input reference signals. We consider step, ramp, and sinusoidal signals, and for each type of the signals we derive a closed form expression for the minimum tracking error attainable by any stabilizing controller. Our results display an explicit dependence of the tracking error on nonminimum phase zeros, unstable poles, and in particular the coupling between the directions of the poles and zeros, and those of the input reference signal, upon which a number of useful conclusions can be drawn. One interesting outcome is that not only zero and pole locations affect tracking performance, but their directional properties also play an important role. The paper provides a nontrivial extension of the previously available results to discrete-time systems, with a consideration on broader classes of reference inputs. Index Terms--MIMO discrete-time systems, nonminimum phase zeros, optimal tracking error, time delays, tracking performance, unstable poles.

In this paper, the following robust control problems are shown to be NP-hard: given a purely complex uncertainty structure [Delta], determine if: 1) [[Mu].sub.[Delta]](M) < 1, for a given rational matrix M; 2) [[M([center dot])]] < 1, for a given rational transfer matrix M(s); and 3) [inf.sub.[Q[element of]H.sup.[infinity]]] [[[F(T, Q)]].sub.[Mu]] < 1, for a given linear fractional transformation F(T, Q) with rational coefficients. In other words, purely complex [Mu] computation, analysis, and synthesis problems are NP-hard. It is also shown that checking 4) stability and 5) computing the [H.sup.[infinity]] norm of a multidimensional system, are NP-hard problems. Therefore, it is rather unlikely to find nonconservative polynomial time algorithms for solving problems 1)-5) in complete generality. Index Terms - Complex structured singular value, computational complexity, [Mu] analysis/synthesis, multidimensional systems, NP-hardness.

In this paper, simultaneous strong stabilization problem is considered, and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator, in terms of the plant orders. A similar problem was also considered in [11], where it was shown that such a bound does not exist for the strong stabilization problem of a single plant. But the examples given in [11] were forcing an approximate unstable pole-zero cancellation or forcing the distance between two distinct unstable zeros to go to zero. In this paper it is shown that: i) If approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeros are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator, and ii) for the simultaneous strong stabilization problem (even for the two plant case), such a bound cannot be found.

This paper presents a simple formula for [H.sup.[infinity]] optimal and suboptimal controllers for unstable SISO distributed plants, with rational weighting functions. The controller is expressed in terms of i) inner and outer parts of the plant, ii) a finite dimensional spectral factor obtained from the weighting functions, and iii) a rational function satisfying certain interpolation conditions. Under certain genericity assumptions this rational function is of dimension less than or equal to [n.sub.1] + l - 1 ([n.sub.1] + l in the suboptimal case), where l is the number of unstable poles of the plant and [n.sub.1] is the order of the sensitivity weighting function. There are 2([n.sub.1] + 1) (2([n.sub.1] + l + 1) in the suboptimal case) linear equations, which determine this rational function. These linear equations can be written directly from the structure of the controller.