TAILIEUCHUNG - Lecture Notes on Linear System Theory

Lecture Notes on Linear System Theory, linear system theory: Introduction, introduction to Algebra, introduction to Analysis, time varying linear systems Solutions, Time invariant linear systems, Solutions and transfer functions,. | Lecture Notes on Linear System Theory John Lygeros and Federico A. Rampond Automatic Control Laboratory ETH Zurich CH-8092 Zurich Switzerland lygeros@ Department of Information Engineering University of Brescia Via Branze 38 25123 Brescia Italy January 3 2015 Contents 1 Introduction 1 Objectives of the course. 1 Proof methods . 2 Functions and maps. 8 2 Introduction to Algebra 11 Groups. 11 Rings and fields. 12 Linear spaces. 15 Subspaces and bases. 17 Linear maps . 21 Linear maps generated by matrices. 24 Matrix representation of linear maps . 25 Change of basis . 27 3 Introduction to Analysis 33 Norms and continuity . 33 Equivalent norms . 35 Infinite-dimensional normed spaces. 38 Completeness. 39 Induced norms and matrix norms . 43 Ordinary differential equations . 46 Existence and uniqueness of solutions . 51 Background lemmas . 51 Proof of existence . 53 Proof of uniqueness . 56 4 Time varying linear systems Solutions 59 Motivation Linearization about a trajectory . 59 i Existence and structure of solutions . 61 State transition matrix. 63 5 Time invariant linear systems Solutions and transfer functions 70 Time domain solution. 70 Semi-simple matrices. 71 Jordan form . 74 Laplace transforms . 77 6 Stability 85 Nonlinear systems Basic definitions. 85 Linear time varying systems. 93 Linear time invariant systems. 95 Systems with inputs and outputs . 98 Lyapunov equation . 100 7 Inner product spaces 104 Inner product . 104 The space of square-integrable functions . 106 Orthogonal complement . 107 Adjoint of a linear map . 109 Finite rank lemma . 112 Application Matrix pseudo-inverse . 114 8 Controllability and observability 118 Nonlinear systems . 118 Linear time varying systems Controllability . 121 Linear time varying systems Minimum energy .

• Tự động hoá
• Lecture Notes on Linear System Theory
• Linear system theory
• Introduction to Algebra
• Introduction to Analysis
• Time varying linear systems
• Time invariant linear systems
• Signals systems
• Lecture Signals systems
• Time invariant system models
• System models in continuous
• Linear system models
• State–space models
• Energy spectral density
• State Space Models
• Matrix exponential
• Transfer function
• Observers for state estimation
• State feedback
• Observer based feedback
• Probabilistic models
• Random variables
• Correlation coefficient
• LTI filtering
• WSS processes
• Power Spectral Density
• Wiener filtering
• Wiener filtering illustrations
• Hypothesis testing
• Neyman Pearson testing
• Signal detection
• Matched filtering