1 Introduction . 1 1.1 Trends of Nonlinear Control System Theory . 1 1.2 Approximate Linearization of the Nonlinear Systems. 4 1.3 Exact Linearization of the Nonlinear Systems . 5 2 Basic Mathematics for Linearization .

7 2.1 Vector Calculus . 7 2.2 State Transformation . 10 2.3 Nonsingular State Feedback . 12 2.4 Vector Field and Tangent Vector .

14 2.5 Covector Field and One-Form . 36 2.6 Distribution and Frobenius Theorem . 39 2.7 State Equivalence and Feedback Equivalence . 56 2.8 MATLAB Programs .

63 2.9 Problems . 69 3 Linearization by State Transformation . 75 3.1 Introduction . 75 3.2 Single Input Nonlinear Systems. 76 3.

3 Multi Input Nonlinear Systems . 83 3.4 MATLAB Programs . 88 3.5 Problems . 91 4 Feedback Linearization . 95 4.1 Introduction .

95 4.2 Single Input Nonlinear Systems. 97 4.3 Multi Input Nonlinear Systems . 110 4.4 Applications of Feedback Linearization . 129 4.5 MATLAB Programs .

138 4.6 Problems . 148 5 Linearization with Output Equation. 153 5.1 Introduction . 153 5.2 State Equivalence to a SISO linear system . 156 5.

3 State Equivalence to a MIMO linear system. 159 5.4 Feedback Linearization with Output of SISO Systems . 162 5.5 Input-Output Linearization of MIMO Systems . 174 5.5.1 Introduction.

174 5.5.2 Structure Algorithm . 180 5.5.3 Conditions for input-output linearization . 185 5.6 Feedback Linearization with Multi Output.

191 5.7 MATLAB Programs . 202 5.8 Problems . 212 6 Dynamic Feedback Linearization . 217 6.1 Introduction . 217 6.

2 Preliminary . 221 6.3 Restricted Dynamic Feedback Linearization . 226 6.4 Examples . 240 6.5 MATLAB Programs . 245 6.

6 Problems . 249 7 Linearization of Discrete-time Systems . 253 7.1 Introduction . 253 7.2 Single Input Discrete-time Systems. 259 7.3 Multi Input Discrete-time Systems .

276 7.4 Linearization of Discrete-time Systems with Single Output. 294 7.5 MATLAB Programs . 306 7.6 Problems . 314 8 Observer Error Linearization . 319 8.

1 Introduction . 319 8.2 Single Output Observer Error Linearization. 322 8.3 Dynamic Observer Error Linearization. 339 8.4 Multi Output Observer Error Linearization . 356 8.

5 Discrete Time Observer Error Linearization . 401 8.6 Discrete Time Dynamic Observer Error Linearization . 425 8.7 MATLAB Programs . 464 8.8 Problems . 501 9 Input-output Decoupling .

509 9.1 Introduction . 509 9.2 Input-output Decoupling of the Nonlinear Systems. 510 9.3 Dynamic Input-output Decoupling . 515 9.4 MATLAB Programs .

533 9.5 Problems . 538 A Basics of Topology. 547 A.1 Topology of Real Numbers. 547 A.2 General Topology . 548 B Manifold .

553 B.1 Vector Space and Algebra . 554 B.2 Vector Fields on Manifolds . 556 C MATLAB Subfunctions. 561.