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In this paper we continue the investigations begun in [13] and [14] on the control of robot manipulators. Using the theory of uncertain dynamical systems developed in [4], [5], [16], [17] we derive a robust nonlinear control strategy with guaranteed tracking properties which can be quantified given bounds on the extent of model uncertainty, sensor noise, input disturbances, etc. We also extend the class of pointwise optimal control strategies of [13] to the case of systems with uncertainty in order to treat the problem of input constraints within the context of uncertain systems.

Structural properties necessary to guarantee the existence of a stabilizing feedback control law for systems described by a set of linear time-invariant differential equations with bounded but unknown time-varying uncertanties are investigated. A monotone mapping theorem is used to explore the relation between an optimal regulator problem with and without uncertainty, and a set of generalized matching conditions are presented which insure that stabilizing feedback gains can be found. Finally, a numerically stable algorithm is presented for computing the generalized matching conditions.

In this paper we study the relationship between the stability boundary of the system (original system), x = y, My = -Dy-f(x) and the stability boundary of the system (reduced system) x = -f(x), where x, y ? Rn and M, D are positive diagonal matrices. A level surface which can be used to approximate the stability boundary of the reduced system will be evaluated.

In this paper we analyze the effects of time-varying forcing functions on the stability boundaries of dissipative pendulum systems. In particular, we model the forcing as "exponentially decaying sinusoids" and show conditions when the stability domains start to break up. Concepts in fractal geometry are needed to better understand these special deformations.

An algorithm is presented which computes the invariant canonical form [1], [2], for a linear multivariable system in state-space form and the transformation matrices which produce this canonical form. An example is given of the algorithm.

This paper explores the relationship between the actual domain of attraction of the swing equations of electric power systems and that of the associated gradient system. A directly implementable on-line test for instability is proposed together with an iterative method guaranteed to improve estimates of the domain of attraction.

French researchers have recently introduced the concept of "secondary" voltage-VAR control based on "pilot points". Operator control of the input reference values on primary AVR's is termed secondary, voltage-VAR control. The French have proposed that such secondary control can be automated by monitoring certain key buses and making adjustments based on these "pilot point" voltages. The pilot points and the control strategy proposed are based on engineering intuition. We pose the problem of determining the optimal pilot point or points as an optimization problem using a Chebyshev norm. That is, we seek a pilot point and a control strategy that will minimize the maximum voltage deviation under a class of disturbances. If all voltage magnitudes are monitored we show that optimal secondary control is achieved through the solution of an overdefined set of equations in the Chebyshev sense. Various control strategies based on less information (a number of pilot points) are investigated including the original French strategy. As an example of optimal pilot point for the IEEE 30 bus test system is determined.