Lur'e problems are historical ones dating back to the 60's, where uncertainties were taken into account only in nonlinear parts. In recent years, however, some new aspects are brought into the problems by taking uncertainties in linear parts as well, into consideration. A possible way to express these uncertainties in input-output relations is to use interval plants described by ratios of two interval polynomials. It is revealed recently that in order to guarantee absolute stability of a Lur'e system with an interval plant using the circle criterion, checking the condition of the criterion for only 16 extreme plants suffices. In this paper, we attempt to prove a parallel result for the Popov criterion. We show that the condition of Popov's theorem for the entire interval plant can be met by checking only 16 extreme plants. A numerical example is presented to illustrate the result.
This paper studies in the framework of transfer matrices the block decoupling problem for linear systems over unique factorization domains. Necessary and sufficient conditions for an injective linear system to be block-decouplable by static feedback are obtained. Moreover the decoupling static state feedback is given. It is shown that the result obtained here is a generalization of the result given by Datta and Hautus in 1984, for systems over unique factorization domains having the same numbers of input and output. Further it is shown that the present result is a generalization of the conditions given by Hautus and Heymann in 1983 for systems over the field of reals.
This paper proposes a method to measure the position and heading of a vehicle on the road by use of the laser and corner cubes. The method uses the laser transmitter and receiver on the vehicle and a line of the retroreflecting targets on a side of the course. The on-board computer calculates the position and heading from the time data when the laser beams hits the corner cube. Each laser beam is set with a certain angle and an offset distance. Then, the time data when the laser beams return to the transmitter vary according to the position and heading of the moving vehicle. After corner cubes are detected by retroreflected laser beam, position and heading are calculated easily. The measured data will be used as the information for compensation of autonomous position computing system as well as for the alert of sleeping to the driver of the automobile.
A simple and efficient algorithm to obtain output feedback gain matrix by pole assignment is presented. This algorithm is based on the continuation method. In the continuation method the given problem is embedded into one parameter family of pole assignment problems and a path joining the initial known solution to the desired solution is traced. The original problem is reduced to the one of assigning the coefficients of the characteristic equation. The relations between the coefficients and the elements of the gain matrix are used fully to derive the homotopy function, from which simple path tracing algorithm is derived. The method requires neither computation of eigenfunctions nor eigen vectors of matrices, so that it is more efficient than the existing method based on continuation method. The efficiency of the algorithm is shown by several numerical examples.
We consider decentralized state feedback control of large-scale discrete event systems consisting of several subsystems which operate concurrently. A (global) control specification is assumed to be given by a predicate. First, we study the relationship between the controllability with respect to entire systems and that with respect to subsystems, which is important for the synthesis of decentralized state feedbacks for large-scale discrete event systems. Next, we derive a necessary and sufficient condition for a decentralized state feedback to achieve the global optimal predicate achievable by a global state feedback. Especially, in the case that a control specification can be reduced to the simultaneous satisfaction of local control specifications, we can design each local state feedback based upon the corresponding local specification.