Model-Based Processing

3State‐Space Models for Identification

3.1 Introduction

State‐space models are easily generalized to multichannel, nonstationary, and nonlinear processes [1–23]. They are very popular for model‐based signal processing primarily because most physical phenomena modeled by mathematical relations naturally occur in state‐space form (see [15] for details). With this motivation in mind, let us proceed to investigate the state‐space representation in a more general form to at least “touch” on its inherent richness. We start with continuous‐time systems and then proceed to the sampled‐data system that evolves from digitization followed by the purely discrete‐time representation – the primary focus of this text.

3.2 Continuous‐Time State‐Space Models

We begin by formally defining the concept of state [1] . The state of a system at time is the “minimum” set of variables (state variables) along with the input sufficient to uniquely specify the dynamic system behavior for all over the interval . The state vector is the collection of state variables into a single vector. The idea of a minimal set of state variables is critical, and all techniques to define them must ensure that the smallest ...