Stabilization of behaviours

In this paper we characterize the set of all restrictions on the behaviour of a plant that shape the characteristic polynomial of the closed-loop system. These control laws include both classical feedback laws and singular feedback laws. One of the results is the behavioural version of the Youla-Jabr-Bongiorno-Kucera-parameterization of all stabilizing control laws for a given plant. We also study robust stability, deriving the real and complex stability radius for systems described in kernel representation. Finally we characterize the set of all control laws that make the stability radius greater than or equal to some desired leve

Saliency Based Control in Random Feature Networks

The ability to rapidly focus attention and react to salient environmental features enables animals to move agiley through their habitats. To replicate this kind of high-performance control of movement in synthetic systems, we propose a new approach to feedback control that bases control actions on randomly perceived features. Connections will be made with recent work incorporating communication protocols into networked control systems. The concepts of {\em random channel controllability} and {\em random channel observability} for LTI control systems are introduced and studied.Comment: 9 pages, 2 figure

Decentralized pole assignment for interconnected systems

Given a general proper interconnected system, this paper aims to design a LTI decentralized controller to place the modes of the closed-loop system at pre-determined locations. To this end, it is first assumed that the structural graph of the system is strongly connected. Then, it is shown applying generic static local controllers to any number of subsystems will not introduce new decentralized fixed modes (DFM) in the resultant system, although it has fewer inputoutput stations compared to the original system. This means that if there are some subsystems whose control costs are highly dependent on the complexity of the control law, then generic static controllers can be applied to such subsystems, without changing the characteristics of the system in terms of the fixed modes. As a direct application of this result, in the case when the system has no DFMs, one can apply generic static controllers to all but one subsystem, and the resultant system will be controllable and observable through that subsystem. Now, a simple observer-based local controller corresponding to this subsystem can be designed to displace the modes of the entire system arbitrarily. Similar results can also be attained for a system whose structural graph is not strongly connected. It is worth mentioning that similar concepts are deployed in the literature for the special case of strictly proper systems, but as noted in the relevant papers, extension of the results to general proper systems is not trivial. This demonstrates the significance of the present work

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

ℒ2-Gain of double integrators with saturation nonlinearity

This note uses quadratic surface Lyapunov functions (SuLFs) to efficiently check if a double integrator in feedback with a saturation nonlinearity has ℒ2-gain less than γ > 0. We show that for many such systems, the ℒ2-gain is nonconservative in the sense that this is approximately equal to the lower bound obtained by replacing the saturation with a constant gain of 1. These results allow the use of classical analysis tools like µ-analysis or integral quadratic constraints to analyze systems with double integrators and saturations, including servo systems like some mechanical systems, satellites, hard disks, compact disk players, etc