An LMI approach to guaranteed cost control for uncertain linear neutral delay systems

This paper considers the problem of guaranteed cost control for uncertain neutral delay systems with a quadratic cost function. The system under consideration is subject to norm‐bounded time‐varying parametric uncertainty appearing in all the matrices of the state‐space model. The problem we address is the design of a state feedback controller such that the closed‐loop system is not only stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is given in terms of a linear matrix inequality (LMI). When this condition is feasible, the desired state feedback controller gain matrices can be obtained via convex optimization. An illustrative example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Inverse Routh table construction and stability of delay equations

Based on an inversion of the Routh table construction, a unimodular characterization of all Hurwitz polynomials is obtained. In parameter space, the Hurwitz polynomials of degree n correspond to the positive 2ⁿ-tant. The method is then used to construct classes of stable continuous-time delay-difference equations and delay differential equations of neutral type, by a suitable limiting process.     

Experimental investigation and biomechanical analysis of lower limb movements for clutch pedal operation

Lower limb movements for clutch-pedal operations were investigated and the influence of four parameters (seat height, pedal travel, pedal travel inclination, pedal resistance) was studied using a multi-adjustable experimental seat. Fifteen subjects participated in the experiment: five short females, five average height males and five tall males. A biomechanical model has been proposed to explain how pedal force direction could be controlled. The experimental observations show that the lower limb movement of clutch pedal operation is mainly guided by the geometric constraints imposed by the task and its environment, especially during the depression phase. The results support the hypothesis that movements obey the principle of minimum work and minimum discomfort. Furthermore, it seems that a functional segmentation exists between the distal joint (ankle) and the proximal joints (knee and hip), thus simplifying the control problem, which is due to the redundancy of the human body. It appears that the depression movement is controlled by proprioceptive feedback related to foot displacement and pedal force, from the fact that the deceleration duration during the depression phase increases with the pedal resistance and pedal travel. The minimum pedal resistance and pedal travel are discussed.     

On the linear quadratic minimum-time problem

A nontraditional minimum-time problem that includes quadratic-state and control-weighting terms in the performance index is investigated. This formulation provides a convenient solution to the problem that uses the solution of the Riccati equation to compute the optimal feedback gain and the optimal time. In some cases the latter is simply found using the derivative of the Riccati equation solution     

Structure and parametrization of periodic linear systems

In this paper, the beginnings of a structure theory for discrete-time periodic linear systems are developed. Canonical forms for state space realizations are described, structural invariants and their combinatorics are studied and geometric aspects of the parametrization of periodic systems are treated.     

Vibrational control of nonlinear time lag systems with boundeddelay: averaging theory, stabilizability, and transient behavior

This paper develops the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay. Averaging theory for fast oscillating, differential delay equations is presented and then applied to vibrational control. Conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems. Transient behavior is also discussed. Illustrative examples are given which show 1) the feasibility of the theory to important applications and 2) the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations     

A note on the cross Riccatian and related properties for symmetricstochastic realizations

Recent results concerning cross Grammians for both SISO (single-input, single-output) and symmetric MIMO (multi-input, multioutput) systems are extended for time-invariant stochastic systems. The extension is based on a cross Riccatian matrix and several results from stochastic realization theory. It is shown that the cross Riccatian can be obtained from the solution to a cross-Riccati equation carrying properties from both a forward and a backwards innovations representation. Other symmetry properties similar to those of the cross Grammian are introduced, along with their connection to balanced stochastic realizations     

On generalized balanced realizations

The class of analytic time-varying linear systems is considered. Different balanced realizations of such systems are defined, and their existence and properties are analyzed. The results are then used to derive reduced order approximations (also for unstable systems). A method is suggested to determine the order of a "good" approximation.