This paper provides the barely essential system-theoretical foundations. Basically, its goal is to introduce the notion of dynamic system and one of its simplest specialisations, namely the discrete-time linear time-invariant case. To overcome such a problem, the choice was made to provide just the most important ideas in a manner deliberately abstracted from their utilisation, with just some proof sketches when relevant, and having the sole purpose of maintaining a consistent treatise.

Chapter Contents:

• 2.1 Dynamic systems
• 2.1.1 State-space representation
• 2.1.2 Motion, equilibrium, stability
• 2.2 The linear time-invariant (LTI) case
• 2.2.1 Motion and equilibrium
• 2.2.2 Stability
• 2.3 Input-output representation of LTI systems
• 2.3.1 The Ƶ transform
• 2.3.2 The transfer function
• 2.3.3 Block diagrams
• 2.3.3.1 Series connection
• 2.3.3.2 Parallel connection
• 2.3.3.3 Feedback (loop) connection
• 2.4 The frequency response
• 2.4.1 Definition
• 2.4.2 Interpretation and use
• 2.5 Time domain responses
• 2.5.1 Impulse response of FIR systems
• 2.5.2 Impulse response of IIR systems
• 2.5.3 Step response of FIR and IIR systems
• 2.6 Concluding remarks
• 2.7 Problems

Inspec keywords: discrete time systems

Other keywords: discrete-time linear time-invariant system; dynamic system; systems theory

Subjects: Discrete control systems