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This paper explores the possibility of constructing two-terminal mechanical devices (one-ports) which are lossless and adjustable. To be lossless, the device must be passive (i.e., not requiring a power supply) and nondissipative. To be adjustable, a parameter of the device should be freely variable in real time as a control input. For the simplest lossless one-ports, the spring and inerter, the question is whether the stiffness and inertance may be varied freely in a lossless manner. We will show that the typical laws which have been proposed for adjustable springs and inerters are necessarily active, and that it is not straightforward to modify them to achieve losslessness, or indeed, passivity. By means of a physical construction using a lever with moveable fulcrum, we will derive device laws for adjustable springs and inerters which satisfy a formal definition of losslessness. We further provide a construction method which does not require a power supply for physically realizable translational and rotary springs and inerters. The analogous questions for lossless adjustable electrical devices are examined.

In this paper, the control of linear parameter-varying (LPV) systems with time-varying real uncertain parameters, where only some of the parameters are measured and available for feedback, is considered. The control objectives are internal stability and disturbance attenuation in the sense of a bounded induced [L.sub.2]-norm from the disturbance to the controlled output. Using parametric Lyapunov functions, the solvability conditions for dynamic output feedback controllers that depend on the measured parameters are expressed in terms of a set of linear matrix inequalities (LMI's) and an additional coupling constraint which destroys the convexity of the overall problem. By transforming the coupling constraint into a rank condition, the problem is recast into a rank-minimization problem with LMI constraints. An example is included that demonstrates the application of the results. Index Terms - Parameter varying systems, robustness.

This paper deals with the design of compensators that provide a guaranteed level of performance, in the sense of [L.sub.2] gain, for systems with time-varying structured uncertainty. For stability, the notion of quadratic stability, using a single Lyapunov function, is used. The uncertainty is assumed to be polytopic (e.g., the uncertainty vector enters the state-space representation of the systems affinely). Recent results in the characterization of [H.sub.infinity] controllers are used to show that quadratic stability with performance is equivalent to a bi-affine problem. A set of conditions, under which the problem becomes convex, is discussed. Index Terms - Output feedback, robust control, structured uncertainty.

This note concerns the effects of observers on robust linear feedback controllers. Sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback. We also study the effects of the resulting high gain observers on the disturbance rejection bounds. We show that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection. However, if there is only an additive plant disturbance and no measurement disturbance, this degradation can be prevented.

Scales are used to reduce the conservatism encountered in most multiobjective approaches. The most general case (i.e., matrix scales) results in a nonconvex problem, though the use of scalar scales leads to convex searches in the analysis and state feedback problems. Output feedback synthesis and other extensions are discussed. Numerical examples are provided to show the effectiveness of the suggested approach. Index Terms--Multiobjective control, scaled Lyapunov matrix.