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The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.
Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems.
Multivariable Computer-controlled Systems is divided into three parts:
Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters.
Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems).
Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models stability stochastic methods H2 optimization and L2 design).
Appendices covering basic mathematical formulae and the description of two MatLAB toolboxes round out this self-contained guide to multivariable control systems.
Of special interest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.
Front Matter.
Polynomial Matrices.
Fractional Rational Matrices.
Normal Rational Matrices.
Front Matter.
Assignment of Eigenvalues and Eigenstructures by Polynomial Methods.
Fundamentals for Control of Causal Discrete-time LTI Processes.
Front Matter.
Parametric Discrete-time Models of Continuous-time Multivariable Processes.
Mathematical Description, Stability and Stabilisation of the Standard Sampled-data System in Continuous Time.
Analysis and Synthesis of SD Systems Under Stochastic Excitation.
H 2 Optimisation of a Single-loop Multivariable SD System.
$$ \mathcal{L}_2 $$ -Design of SD Systems for 0 &lt t &lt ∞