Mathematical Linear System Theory

This series learns the theoretical meaning and operation methods of linear systems by studying the state space, state space, transfer function matrix, etc. of linear systems. Use the state space method as the main tool to study the theory of multi-variable linear systems. After the 1950s, with the development of aerospace and other technologies and the expansion of the application scope of control theory, the limitations of classical linear control theory have become increasingly obvious. It can neither meet practical needs nor solve some problems raised by the theory itself. This has promoted The study of linear systems began, and it developed from the classical stage to the current stage after 1960. American scholar RE Kalman first applied the state space method to the study of multi-variable linear systems and proposed two basic concepts of controllability and observability. After the 1960s, modern linear system theory has made new developments, and new theories and methods for studying multivariable systems have emerged, such as linear system geometric theory, linear system algebraic theory, and multivariable frequency domain methods.

• Chapter 1：Matrix polynomials and matrix functions (1) (22 minutes and 51 seconds)

• Chapter 2：Matrix polynomials and matrix functions (2) (23 minutes and 49 seconds)

• Chapter 3：Matrix polynomials and matrix functions (3) (22 minutes and 58 seconds)

• Chapter 4：Matrix polynomials and matrix functions (4) (22 minutes and 6 seconds)

• Chapter 5：State space model of the system (1) (22 minutes and 18 seconds)

• Chapter 6：State space model of the system (2) (24 minutes and 11 seconds)

• Chapter 7：State space model of the system (3) (23 minutes and 50 seconds)

• Chapter 8：State space model of the system (4) (24 minutes and 6 seconds)

• Chapter 9：System status response and output response (1) (24 minutes and 36 seconds)

• Chapter 10：System status response and output response (2) (23 minutes and 0 seconds)

• Chapter 11：System status response and output response (3) (24 minutes and 36 seconds)

• Chapter 12：System status response and output response (4) (23 minutes and 49 seconds)

• Chapter 13：System status response and output response (5) (22 minutes and 59 seconds)

• Chapter 14：System status response and output response (6) (23 minutes and 33 seconds)

• Chapter 15：System status response and output response (7) (22 minutes and 25 seconds)

• Chapter 16：System status response and output response (8) (22 minutes and 51 seconds)

• Chapter 17：System status response and output response (9) (22 minutes and 9 seconds)

• Chapter 18：System status response and output response (10) (23 minutes and 2 seconds)

• Chapter 19：System controllability and observability (1) (24 minutes and 5 seconds)

• Chapter 20：System controllability and observability (2) (22 minutes and 28 seconds)

• Chapter 21：System controllability and observability (3) (24 minutes and 41 seconds)

• Chapter 22：System controllability and observability (4) (22 minutes and 34 seconds)

• Chapter 23：System controllability and observability (5) (22 minutes and 17 seconds)

• Chapter 24：System controllability and observability (6) (23 minutes and 4 seconds)

• Chapter 25：System controllability and observability (7) (22 minutes and 2 seconds)

• Chapter 26：System controllability and observability (8) (23 minutes and 14 seconds)

• Chapter 27：System controllability and observability (9) (24 minutes and 2 seconds)

• Chapter 28：System controllability and observability (10) (22 minutes and 4 seconds)

• Chapter 29：State space implementation of transfer function matrix (1) (22 minutes and 47 seconds)

• Chapter 30：State space implementation of transfer function matrix (2) (22 minutes and 47 seconds)

• Chapter 31：State space implementation of transfer function matrix (3) (22 minutes and 18 seconds)

• Chapter 32：State space implementation of transfer function matrix (4) (23 minutes and 55 seconds)

• Chapter 33：State space implementation of transfer function matrix (5) (22 minutes and 3 seconds)

• Chapter 34：System stability (1) (24 minutes and 4 seconds)

• Chapter 35：System stability (2) (22 minutes and 37 seconds)

• Chapter 36：System stability (3) (22 minutes and 2 seconds)

• Chapter 37：System stability (4) (22 minutes and 55 seconds)

• Chapter 38：System stability (5) (22 minutes and 42 seconds)

• Chapter 39：System stability (6) (24 minutes and 0 seconds)

• Chapter 40：System stability (7) (24 minutes and 59 seconds)

• Chapter 41：System stability (8) (24 minutes and 56 seconds)

• Chapter 42：System stability (9) (22 minutes and 27 seconds)

• Chapter 43：System stability (10) (24 minutes and 59 seconds)

• Chapter 44：System stability (11) (23 minutes and 46 seconds)

• Chapter 45：System stability (12) (23 minutes and 53 seconds)

• Chapter 46：System stability (13) (24 minutes and 37 seconds)

• Chapter 47：System stability (14) (24 minutes and 57 seconds)

• Chapter 48：State feedback and state observer (1) (22 minutes and 7 seconds)

• Chapter 49：State feedback and state observer (2) (24 minutes and 10 seconds)

• Chapter 50：Status feedback and status observer (3) (22 minutes and 15 seconds)

• Chapter 51：State feedback and state observer (4) (23 minutes and 22 seconds)

• Chapter 52：State feedback and state observer (5) (24 minutes and 36 seconds)

• Chapter 53：State feedback and state observer (6) (22 minutes and 11 seconds)

• Chapter 54：State feedback and state observer (7) (23 minutes and 13 seconds)