Modern Control System TheoryAbout the book... The book provides an integrated treatment of continuoustime and discretetime systems for two courses at postgraduate level, or one course at undergraduate and one course at postgraduate level. It covers mainly two areas of modern control theory, namely; system theory, and multivariable and optimal control. The coverage of the former is quite exhaustive while that of latter is adequate with significant provision of the necessary topics that enables a research student to comprehend various technical papers. The stress is on interdisciplinary nature of the subject. Practical control problems from various engineering disciplines have been drawn to illustrate the potential concepts. Most of the theoretical results have been presented in a manner suitable for digital computer programming along with the necessary algorithms for numerical computations. 
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Contents
Introduction  1 
Linear Spaces and Linear Operators  10 
CHAPTER 3  29 
CHAPTERS  40 
3  55 
State Variable Descriptions  64 
State Equations for Dynamic Systems  72 
Nonuniqueness of State Model  82 
6  195 
Controllability and Observability  200 
2  222 
Descriptions  262 
Linear TimeInvariant DiscreteTime Systems  270 
Stability  312 
Model Control  372 
CONTENTS  418 
Concluding Comments  89 
References  98 
Linear DiscreteTime Models  113 
Concluding Comments  135 
References  144 
Equations  152 
System Modes  173 
Optimal Feedback Control  497 
Linear Regulator with a Prescribed Degree  549 
Stochastic Optimal Linear Estimation and Control  590 
CONTENTS  627 
Answers and Aids to Problems  641 
Index  673 
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Common terms and phrases
algorithm assume asymptotically stable boundary conditions canonical form Chapter characteristic polynomial closedloop system coefficients column companion form constant matrix continuoustime systems control system control theory controllable and observable defined determine differential equation digital computer discretetime discretetime systems dynamic eigenvalues eigenvectors elements energy Example exists feedback control finite given by eqn gives IEEE Trans initial conditions input integral Kalman linear operator linear regulator linear system linear timeinvariant system linearly independent Lyapunov function matrix exponential method minimizes minimum n x n nonlinear nonsingular obtain optimal control optimal control law performance index plant positive definite real constant real numbers refer eqn regulator problem representation respectively result Riccati equation satisfies scalar Section shown in Fig solve square matrix stability steadystate system described system of Fig tank Theorem timevarying trajectory transfer function transformation transition matrix variables vector space voltage zero