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Session 1 Linear Control Systems. Examples. Linearization. Transition Matrix. Reading Assignment Rugh (1996 edition) chapters 1-4 and scan Chapter 20 until Example 20.7. The main new thing is to do linearization along a trajectory rather than at an equilibrium, and the definition and properties of the transition matrix Φ(t, τ). Exercise 1.1 = Rugh 1.9 Exercise 1.2 = Rugh 1.20 (spectral norm) Exerc

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/2019LinearSystem/2019_Linear_System_Exercise_1.pdf - 2025-06-29

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Session 3 Reachability and Controllability. Observability and Reconstructability. Controller and Observer Forms. Reading Assignment Rugh, Ch 9, 13, 14 (only Theorem 14.9) (for continuous-time systems) and Ch 25 (for discrete-time systems). Exercise 3.1 = Rugh 9.1. Exercise 3.2 = Rugh 9.2 Exercise 3.3 = Rugh 9.4 Exercise 3.4 = Rugh 9.5 Exercise 3.5 = Rugh 9.7 Exercise 3.6 a. Show that {A,B} is cont

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/2019LinearSystem/2019_Linear_System_Exercise_3.pdf - 2025-06-29

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Session 5 LTV stability. Quadratic Lyapunov functions. Reading Assignment Rugh Ch 6,7,12 (skip proofs of 7.8, 12.6 and 12.7),14 (pp240-247), and (22,23,24,28) Exercise 5.1 = Rugh 6.3 iii+iv Exercise 5.2 = Rugh 6.11 Exercise 5.3 = Rugh 7.3 Exercise 5.4 = Rugh 8.3 Exercise 5.5 = Rugh 7.6 Exercise 5.6 = Rugh 7.11 Exercise 5.7 = Rugh 7.20 Exercise 5.8 = Rugh 23.2 Hand in problems Exercise 5.9 = Rugh 8

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/2019LinearSystem/2019_Linear_System_Exercise_5.pdf - 2025-06-29

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Session 7 Polynomial Matrix Descriptions, Poles and Zeros of MIMO systems Reading Assignment Rugh, Ch. 16-17. Exercises Exercise 7.1 Make sure you can handle the Maple routines Matrix, Hermite- Form, SmithForm. Hint: ?MatrixPolynomialAlgebra[HermiteForm] gives some help text. Exercise 7.2 = Rugh 16.1 Exercise 7.3 = Rugh 16.2 Exercise 7.4 Determine the Smith form, i.e. the invariant polynomials, fo

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/2019LinearSystem/2019_Linear_System_Exercise_7.pdf - 2025-06-29

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LionSealWhite Linear Systems, 2019 - Lecture 1 Introduction Multivariable Time-varying Systems Transition Matrices Controllability and Observability Realization Theory Stability Theory Linear Feedback Multivariable input/output descriptions Some Bonus Material 1 / 21 LionSealWhite Lecture 1 State equations Linearization Examples Transition matrices Rugh, chapters 1-4 Main news: Linearization aroun

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/2019LinearSystem/2019_Linear_System_Lecture_1.pdf - 2025-06-29

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LionSealWhite Lecture 5 LTV stability concepts Quadratic Lyapunov functions Feedback, Well-posedness, Internal Stability Rugh Ch 6,7,12 (skip proofs of 12.6 and 12.7),14 (pp240-247) + (22,23,24,28) Zhou, Doyle, Glover pp 117-124 1 / 31 LionSealWhite Stability For LTI systems ẋ = Ax the stability concept was easy, we had the two concepts i) Stability: x(t) remains bounded ii) Asymptotic stability:

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/2019LinearSystem/2019_Linear_System_Lecture_5.pdf - 2025-06-29

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LionSealWhite Lecture 7 Theory for polynomial matrices Hermite and Smith normal forms Smith McMillan form Poles and Zeros Rugh Ch 16-17 (can skip proofs of 16.7,17.4,17.5,17.6) 1 / 36 LionSealWhite Polynomial matrix fraction descriptions There are two natural generalisation to the SISO description G(s) = n(s) d(s) Right polyomial matrix fraction description: G(s) = NR(s)DR(s)−1 { DR(s)X(s) = U(s)

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/2019LinearSystem/2019_Linear_System_Lecture_7.pdf - 2025-06-29

Control System Synthesis - Introduction - PhD Class - Fall 2020

Control System Synthesis - Introduction - PhD Class - Fall 2020 Control System Synthesis - Introduction PHD CLASS - FALL 2020 Brief history and motivations The big picture Class overview Content overview 1 Brief history and motivations 2 The big picture 3 Class overview Pauline Kergus - Karl Johan Åström Control System Synthesis 1st September 2020 2/27 Brief history and motivations The big picture

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/ControlSystemsSynthesis/2020/Control_System_Synthesis-introduction.pdf - 2025-06-29