Abstract-This paper investigates string stability issues in homogeneous strings of strictly proper feedback control systems with unidirectional nearest neighbour communications, using only linear systems with two integrators in the loop. We show under which conditions the induced L2-norm of the disturbance to error transfer function is bounded independently of the string length when using a constant time headway and derive a formula for the infimal time headway to guarantee string stability.
Abstract-In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form , , and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of the product ( ). The technical note also contains a spectral characterization of strictly positive real transfer functions which are strictly proper. Examples are presented to illustrate our results.Index Terms-LTI systems.
-This paper investigates string stability issues in homogeneous strings of strictly proper feedback control systems. We consider initial condition problems with unidirectional nearest neighbour communications, using only linear systems with two integrators in the loop. We define string stability as a type of stability that is uniform with respect to the string length. We show conditions under which the L2-norm and the L∞-norm of states are bounded and derive a formula for the minimal time headways required to guarantee string stability.
In this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A − gh T , and where one of the matrices is singular. We then apply this result in a study of a feedback system with a saturating actuator.
The basic theory of supervisory control of discrete-event systems is extended with the notion of templates, which simplifies the modeling of controllers since one can work with conceptual designs. In this work, software which provides support for the new design approach is presented along with its application to a robotic testbed.
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