CONTROLLABILITY AND STABILIZABILITY OF LINEAR SYSTEMS IN HILBERT SPACES

📄 Project Abstract

Questions about controllability and stability arise in almost every dynamical system problem. As a result, controllability and stability are one of the most extensively studied subjects in system theory. A departure point of control theory is the di_x001B_erential equation x_ = f(x; u); x(0) = x0 2 Rn; (1.0.1) with the right hand side depending on a parameter u from a set U _x001A_ Rm. The set U is called the set of control parameters. Controls are of two types: open and closed loops. An open loop control can be basically an arbitrary function u(_x0001_) : [0;+1) ! U; for which the equation x_ (t) = f(x(t); u(t)); t _x0015_ 0; x(0) = x0 2 Rn; (1.0.2) has a well de_x001C_ned solution. A closed loop control can be identi_x001C_ed with a mapping k : Rn ! U, which may depend on t _x0015_ 0, such that the equation x_ (t) = f(x(t); k(x(t))); t _x0015_ 0; x(0) = x0 2 Rn; (1.0.3) has a well de_x001C_ned solution. The mapping k(_x0001_) is called feedback. Controls are called also strategies or...