State observers for linear systems with uncertainty
The book presents the latest achievements in the field of synthesis of asymptotic state observers for dynamical systems described by linear ordinary differential equations or by their discrete-time analogues. Chapter 1 contains the statement of the problem of constructing of a state observer, notions of the asymptotic and finite observers, and notions of the minimal and functional observers. In Chapter 2, the concepts of observability and identifiability are considered for linear dynamical systems of the form \[ \dot{x}=A(t)x+B(t)u, \qquad y=C(t)x, \] where \(x \in \mathbb R^n\) is an unknown state (phase) vector, \(u \in \mathbb R^m\), \(y \in \mathbb R^l\), are known input and output, respectively. Kalman's and Rosenbrock's observability criteria are given for linear stationary systems, and also some canonical forms are described. Chapter 3 presents algorithms of synthesis of full-dimensional state observers for scalar and vector stationary fully determined systems. In Chapter 4, the authors describe new approaches to the synthesis of functional observers of the given order for fully determined systems. They propose an algorithm for synthesizing functional observers of minimal order and obtain lower bounds for the order of the observers. Chapter 5 deals with the problem of asymptotic observers synthesis for linear stationary systems with unknown disturbances \(Df\) in the right-hand part of the state equation. For hyper-output systems two approaches to solving the problem are proposed, namely, the method of quasisplitting and the methods of pseudoinputs. For square systems an approach is proposed which makes it possible to obtain an estimate of the unknown state vector with any preassigned accuracy, but this approach is not asymptotic. In Chapter 6, the observer constructing problem is analyzed for the class of stationary dynamical systems with bilinear term \(uBx\) in the right-hand part of the state equation. Planar (\(x \in \mathbb R^2\)) bilinear systems are considered in detail. For bilinear systems of arbitrary dimension, different cases of degeneration of the bilinearity matrix \(B\) are examined. At last, in Chapter 7, the theory of observers is developed for discrete-time linear systems. It is similar to the theory of observers for continuous-time systems. The book is intended for specialists in control theory as well as for students and post-graduate students of the corresponding specialities.
scientific article; zbMATH DE number 5628240