Abstract
This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.
Highlights
The problems of absolute stability and hyperstability classically received much attention from the fifties in a wide class of problems of control theory and its applications, [1,2,3,4,5,6,7,8,9,10]
The more general problem of asymptotic hyperstability extends that of absolute stability to classes of nonlinear regulators satisfying integral-type constraints for eventually timevarying nonlinearities which are not necessarily constrained to sectors
The asymptotic hyperstability property of a closedloop system requires, in particular, that the feed-forward loop consists of a positive real transfer matrix or function, and that the nonlinear/time-varying controller belongs to a class satisfying an integral-type constraint, the so-called Popovian integral inequality, [15, 16]
Summary
The problems of absolute stability and hyperstability classically received much attention from the fifties in a wide class of problems of control theory and its applications, [1,2,3,4,5,6,7,8,9,10]. Most of the stability problems can be extended to the use of switching laws acting on the controlled objects or on their controllers so that the dynamics can be changed to improve certain suitable performances like, for instance, suited settling times or transient errors, or to accommodate the system behavior to suitable transients around several operation points. This frequently happens in complex dynamic problems associated to distinct phases in some production chains like it occurs, for instance, in some chemical engineering processes.
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