Abstract
The problem of controllability to a given convex target set of a linear time-varying control system on time scales is studied. Necessary and sufficient conditions of controllability with constrained controllers for such a system are given. To this aim the separation theorem is used.
Highlights
Controllability is one of the fundamental concepts in control theory
In [, ] necessary and sufficient conditions for controllability of linear time-varying continuous-time systems with control defined on some subset of Rm not containing zero are proved
One of the main concepts of time scale theory is the delta derivative, which is a generalization of the classical time derivative in the continuous time and the finite forward difference in the discrete time
Summary
Controllability is one of the fundamental concepts in control theory. Kalman’s classic result on the controllability assumes that controls are functions on time with values on some nonempty subset of Rm. One of the main concepts of time scale theory is the delta derivative, which is a generalization of the classical time derivative in the continuous time and the finite forward difference in the discrete time. This allows one to consider delta differential equations on an arbitrary time model. The goal of this paper is to study conditions under which a linear time-varying system with control constrains defined on a time scale is controllable. Section extends the classical notation of constrained controllability to the case of time-varying systems defined on any, nonuniform, model of time. The condition for -controllability given in Section shows that in a stationary case the obtained results can be approximated by the classical exponential function
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