More particularly, the aim is to derive open loop conditions for the boundedness and continuity of feedback systems, without, at the beginning, placing restrictions on linearity or time invariance. The object of this paper is to outline a stability theory for input-output problems using functional methods. Being FTS a quantitative approach, the paper also gives an estimate of the necessary minimum dithering/mixing frequency, and the effectiveness of the proposed finite-time stabilization approach is analy The main advantage of the proposed approach resides in that it is capable of dealing with systems with unknown control direction, and/or with a control direction that changes over time. The finite-time stability (FTS) of the averaged dynamics implies the FTS of the original system, as the distance between the original and the averaged dynamics can be made arbitrarily small by choosing a sufficiently high value of the dithering frequency used by the extremum seeking algorithm. We propose to use a suitable oscillatory input to modify the system dynamics, at least in an average sense, so as to satisfy a Differential Linear Matrix Inequality (DLMI) condition which in turns guarantees that the system's state remains inside a prescribed time varying hyper-ellipsoid in the state space. In this paper the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum seeking algorithm. The applicability of theĭevised results is illustrated through a numerical example. Both conditionsĪre necessary and sufficient, and lead to optimization prob�lems cast in the form of DLMIs. One for stabilization via output feedback. Stabilization via state feedback, followed by a more general The secondĬontribution of the paper is a theorem for IO finite-time The feasibility of an optimization problem by solving a set ofĭifference Linear Matrix Inequalities (DLMIs). Involves the solution of a set of Generalized Difference Lya�punov Equations (GDLEs) the latter allows one to establish Necessary and sufficient conditions for IO-FTS. The first contribution of the paper is a pair of Many discrete-time control problems are defined over aįinite interval of time, therefore the development and appli�cation of finite-time control methodologies is of particular Important role in many engineering contexts. InĬurrent control science, discrete-time systems play a very This work deals with the Input-Output Finite�Time Stability (IO-FTS) of linear discrete-time systems. The effectiveness and computational issues of the two approaches for the analysis and the synthesis, respectively, are discussed in two examples in particular, our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude. We show that the last condition is computationally more efficient however, the formulation via DLMI allows to solve the problem of the IO finite-time stabilization via output feedback. Amato is actually also a necessary condition for IO-FTS at the same time we provide an alternative-still necessary and sufficient-condition for IO-FTS, in this case based on the existence of a suitable solution to a differential Lyapunov equality (DLE). First, by using an approach based on the reachability Gramian theory, we show that the main theorem of F. In this context, this paper presents several novel contributions. IO-FTS constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response. Roughly speaking, a system is said to be input-output finite-time stable if, given a class of norm bounded input signals over a specified time interval of length T, the outputs of the system do not exceed an assigned threshold during such time interval. Amato ) a sufficient condition for input-output finite-time stability (IO-FTS), when the inputs of the system are L2 signals, has been provided such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality (DLMI). In the recent paper “Input-output finite-time stabilization of linear systems,” (F.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |