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Linear and Nonlinear Multivariable Feedback Control by Oleg Gasparyan

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2 Performance and design of linear MIMO systems

2.1 INTRODUCTION

In the first part of this chapter, we shall consider in detail the analysis of steady-state dynamical processes, especially concentrating our attention on the investigation of MIMO systems accuracy under sinusoidal, slowly changing deterministic and stationary random input signals.

Throughout the whole chapter, we shall follow the idea that the accuracy and other performance characteristics of linear MIMO systems of any order N can be evaluated with the help of some scalar values calculated by readily ‘recognizable’ techniques, where the latter are straightforward extensions to the multivariable case of conventional techniques for SISO control systems. To the mentioned scalar values belong:

• magnitude of the vector of error complex amplitudes, under sinusoidal inputs;

• magnitude of the steady-state error vector, under slowly changing deterministic inputs;

• mean square value of the error vector magnitude, under stationary stochastic inputs.

Proceeding in such a way, we shall not stick rigidly to the standard framework of the CTFs method, resorting, when needed, to more wide resources of the functional analysis. Most frequently in these cases, the notion of a transfer matrix norm induced by the Euclidean norm (length) of the vector will be used, as it has already become conventional in modern control theory. At the same time, the relationship between the performance of a linear MIMO system on the whole and that of ...

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