Global Internal Stabilization Research Articles

Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains

We consider a two-component Reaction-Diffusion system posed on non coincident spatial domains and featuring a reaction term involving an integral kernel. The question of global existence of componentwise nonnegative solutions is assessed. Then we investigate the stabilization of one of the solution components to zero via an internal control distributed on a small subdomain while preserving nonnegativity of both components. Our results apply to predator-prey systems.

Global Regulation of Input-Saturated Discrete-Time Linear Systems Subject to Persistent Disturbances

A novel control strategy for globally stabilizing inputsaturated linear plants subject to persistent, arbitrarily large but bounded, disturbances is described. The technique is based on a weaker concept of robust positive invariance, referred to in the paper as positive quasi d-invariance, which is believed to be new and allow the achievement of better control performance if compared with those resulting from using actual control strategies based on the classical notion of positive d-invariance. Simultaneous global internal asymptotic stability and semiglobal external finite-gain BIBO stability is achieved under critical structural conditions on the disturbance-to-state map of the plant. Finally, an example is presented where the achievable regulation performance is shown and contrasted with those achievable by a control solution based on the classical notion of positive d-invariance.

Composition cascade control for chemical reactors

AbstractEventhough the composition control of chemical reactors is an old, widely studied, and still relevant problem in chemical process control, it still presents some aspects that remain unexplored or unresolved. For instance, a unifying approach is needed to systematize the existing ad hoc controller constructions, to rigorously explain their remarkable robustness property, and to explore the possibility of improving their construction and functioning. In this paper, some aspects of these control problems are addressed by resorting to recently developed approaches in constructive non‐linear control, yielding a systematic controller construction coupled to a simple tuning scheme that can be executed with standard tuning rules, a closed‐loop stability criterion, and an explanation of the closed‐loop dynamics behaviour. Specifically, a linear cascade (master/slave) control configuration is proposed, which leads to global internal stability of the controlled system with asymptotic regulation of the output‐stream composition about a given desired setpoint. A simulation example is used to illustrate the results. Copyright © 2002 John Wiley & Sons, Ltd.

Global switching regulation of input-saturated discrete-time linear systems with arbitrary l/sub 2/ disturbances

Monotonicity properties of suboptimal H/sub /spl infin// or minimax control are established and exploited so as to develop a suitable state-feedback switching logic for regulating input-saturated linear plants in the presence of arbitrary l/sub 2/-disturbances. If the plant is asymptotically null controllable with bounded inputs, the scheme is shown to provide simultaneously global internal asymptotic stabilization and global external l/sub 2/ stabilization.

On simultaneous global external and global internal stabilization of critically unstable linear systems with saturating actuators

This paper deals with simultaneous global external as well as global internal stabilization of linear systems with saturating actuators. The paper proposes a new family of scheduled low-and-high gain state feedback laws that yields a closed-loop system that is both globally finite gain L/sub p/ stable and globally asymptotically stable. Moreover, the controller has an explicit design parameter that can be adjusted to make the L/sub p/ gain of the closed-loop system arbitrarily small.

Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems with Saturating Actuators

The issues arising in hybrid or simultaneous external as well as internal stabilization of linear systems with saturating actuators are considered. Four different stabilization problems are studied. Roughly, these problems are (1) simultaneous semi-global external as well as semi-global internal stabilization, (2) simultaneous semi-global external as well as global internal stabilization, (3) simultaneous global external as well as semi-global internal stabilization, and (4) simultaneous global external as well as global internal stabilization. As evident from the literature, the requirement of internal stabilization alone either in the global or semi-global sense demands that the linear part of the given system be (a) stabilizable, and (b) has all its poles in the closed left half complex plane for continuous-time systems while it has all its poles inside and/or on the unit circle for discrete-time systems. This implies that the posed simultaneous stabilization problems are solvable at best only under the conditions (a) and (b). Under such conditions, we construct here explicit state as well as measurement feedback controllers for all the four problems in the case of continuous-time systems, and for the problems (1), (2) and (4) in the case of discrete-time systems. The design methodologies used to construct appropriate feedback laws are based on by now familiar low-gain and low-and-high gain design concepts or certain scheduled versions of them.

Adaptive disturbance attenuation with global stability for rigid and elastic joint robots

The disturbance attenuation problem with global internal stability is solved for both rigid and elastic joint robots in the presence of unknown constant parameters. The proposed dynamic controller combines adaptive and H ∞ control techniques.