Linear System Theory and Design

An extensive revision of the author's highly successful text, this third edition of Linear System Theory and Design has been made more accessible to students from all related backgrounds. After introducing the fundamental properties of linear systems, the text discusses design using state equations and transfer functions. In state-space design, Lyapunov equations are used extensively to design state feedback and state estimators. In the discussion of transfer-function design, pole placement, model matching, and their applications in tracking and disturbance rejection are covered. Both one-and two-degree-of-freedom configurations are used. All designs can be accomplished by solving sets of linear algebraic equations. The two main objectives of the text are to: 1. use simple and efficient methods to develop results and design procedures 2. enable students to employ the results to carry out design All results in this new edition are developed for numerical computation and illustrated using MATLAB, with an emphasis on the ideas behind the computation and interpretation of results. This book develops all theorems and results in a logical way so that readers can gain an intuitive understanding of the theorems. This revised edition begins with the time-invariant case and extends through the time-varying case. It also starts with single-input single-output design and extends to multi-input multi-output design. Striking a balance between theory and applications, Linear System Theory and Design, 3/e, is ideal for use in advanced undergraduate/first-year graduate courses in linear systems and multivariable system design in electrical, mechanical, chemical, and aeronautical engineering departments. It assumes a working knowledge of linear algebra and the Laplace transform and an elementary knowledge of differential equations. 

 

PREFACE ; 1.INTRODUCTION ; 1.1.INTRODUCTION ; 1.2.OVERVIEW ; 2.MATHEMATICAL DESCRIPTIONS OF SYSTEMS ; 2.1.INTRODUCTION ; 2.2.LINEAR SYSTEMS ; 2.3.LINEAR TIME-INVARIANT (LTI) SYSTEMS ; 2.4.LINEARIZATION ; 2.5.EXAMPLES ; 2.6.DISCRETE-TIME SYSTEMS ; 3.LINEAR ALGEBRA ; 3.1.INTRODUCTION ; 3.2.BASIS, REPRESENTATION, AND ORTHONORMALIZATION ; 3.3.LINEAR ALGEBRAIC EQUATIONS ; 3.4.SIMILARITY TRANSFORMATION ; 3.5.DIAGONAL FORM AND JORDAN FORM ; 3.6.FUNCTIONS OF A SQUARE MATRIX ; 3.7.LYAPUNOV EQUATION ; 3.8.SOME USEFUL FORMULA ; 3.9.QUADRATIC FORM AND POSITIVE ; 3.10.SINGULAR VALUE DECOMPOSITION ; 3.11.NORMS OF MATRICES ; 4.STATE-SPACE SOLUTIONS AND REALIZATIONS ; 4.1.INTRODUCTION ; 4.2.SOLUTION OF LTI STATE EQUATIONS ; 4.3.EQUIVALENT STATE EQUATIONS ; 4.4.REALIZATIONS ; 4.5.SOLUTION OF LINEAR TIME-VARYUBG (LTV) EQUATIONS ; 4.6.EQUIVALENT TIME-VARYING EQUATIONS ; 4.7.TIME-VARYING REALIZATIONS ; 5.STABILITY ; 5.1.INTRODUCTION ; 5.2.INPUT-OUTPUT STABILITY OF LTI SYSTEMS ; 5.3.INTERNAL STABILITY ; 5.4.LYAPUNOV THEOREM ; 5.5.STABILITY OF LTV SYSTEMS ; 6.CONTROLLABILITY AND OBSERVABILITY ; 6.1.INTRODUCTION ; 6.2.CONTROLLABILITY ; 6.3.OBSERVABILITY ; 6.4.CANONICAL DECOMPOSITION ; 6.5.CONDITIONS IN JORDAN-FORM EQUATIONS ; 6.6.DISCRETE-TIME STATE EQUATIONS ; 6.7.CONTROLLABILITY AFTER SAMPLING ; 6.8.LTV STATE EQUATIONS ; 7.MINIMAL REALIZATIONS AND COPRIME FRACTIONS ; 7.1.INTRODUCTION ; 7.2.IMPLICATIONS OF COPRIMENESS ; 7.3.COMPUTING COPRIME FRACTIONS ; 7.4.BALANCED REALIZATION ; 7.5.REALIZATIONS FROM MARKOV PARAMETERS ; 7.6.DEGREE OF TRANSFER MATRICES ; 7.7.MINIMAL REALIZATIONS- MATRIX CASE ; 7.8.MATRIX POLYNOMIAL FRACTIONS ; 7.9.REALIZATION FROM MATRIX COPRIME FRACTIONS ; 7.10.REALIZATIONS FROM MATRIX MARKOV PARAMETERS ; 7.11.CONCLUDING REMARKS ; 8.STATE FEEDBACK AND STATE ESTIMATORS ; 8.1.INTRODUCTION ; 8.2.STATE FEEDBACK ; 8.3.REGULATION AND TRACKING ; 8.4.STATE ESTIMATOR ; 8.5.FEEDBACK FROM ESTIMATED STATES ; 8.6.STATE FEEDBACK-MULTIVARIABLE CASE ; 8.7.SATE ESTIMATORS-MULTIVARIABLE CASE ; 8.8.FEEDBACK FROM ESTIMATED STATES-MULTIVARIABLE CASE ; 9.POLE PLACEMENT AND MODEL MATCHING ; 9.1.INTRODUCTION ; 9.2.UNITY-FEEDBACK AND CONFIGURATION-POLE PLACEMENT ; 9.3.IMPLEMENTABLE TRANSFER FUNCTIONS ; 9.4.MULTIVARIABLE UNITY FEEDBACK SYSTEMS ; 9.5.MULTIVARIABLE MODEL MARCHING-TWO-PARAMETER CONFIGURATION ; 9.6.CONCLUDING REMARKS ; REFERENCES ; ANSWERS TO SELECTED PROBLEMS ; INDEX