Contents Introduction LTI Models LTI Models Using LTI Models in the Control System Toolbox LTI Objects Precedence rules 2-5 Viewing LTI Systems As Matrices 2-5 Command Summary 2-6 Creating LTI Model 2-8 Transfer Function Models Zero-Pole- Gain Models 2-12 State-Space Models 2-14 Descriptor State-Space Models 2-16 Frequency Response Data(FRD) Models 2-17 Discrete-Time models 2-19 Data Retrieval 2-23 LTI Properties Generic Properties Model-Specific Properties Setting Lti Properties Accessing Property Values Using get Direct Property Referencing Additional Insight into LTI Properties 2-32 Model Conversion Explicit Conversion 2-40 Automatic Conversion 2-41 Caution about Model conversions 2-41i Contents 1 Introduction 2 LTI Models LTI Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Using LTI Models in the Control System Toolbox . . . . . . . . . . . 2-3 LTI Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Precedence Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Viewing LTI Systems As Matrices . . . . . . . . . . . . . . . . . . . . . . . 2-5 Command Summary . . . ............................... 2-6 Creating LTI Models .................................. 2-8 Transfer Function Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 Zero-Pole-Gain Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12 State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14 Descriptor State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . 2-16 Frequency Response Data (FRD) Models . . . . . . . . . . . . . . . . . 2-17 Discrete-Time Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19 Data Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23 LTI Properties ....................................... 2-25 Generic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25 Model-Specific Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 Setting LTI Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28 Accessing Property Values Using get . . . . . . . . . . . . . . . . . . . . 2-30 Direct Property Referencing . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31 Additional Insight into LTI Properties . . . . . . . . . . . . . . . . . . 2-32 Model Conversion ................................... 2-40 Explicit Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40 Automatic Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41 Caution About Model Conversions . . . . . . . . . . . . . . . . . . . . . . 2-41