An approximation theorem for the algebraic Riccati equation
SIAM Journal on Control and Optimization
An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
System theoretic properties of a class of spatially invariant systems
Automatica (Journal of IFAC)
Discretized partial differential equations: Examples of control systems defined on modules
Automatica (Journal of IFAC)
IEEE Transactions on Information Theory
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In this paper block circulant and block Toeplitz long strings of MIMO systems with finite length are compared with their corresponding infinite-dimensional spatially invariant systems. The focus is on the convergence of the sequence of solutions to the control Riccati equations and the convergence of the sequence of growth bounds of the closed-loop generators. We show that block circulant approximants of infinite-dimensional spatially invariant systems reflect well the LQR behavior of the infinite-dimensional systems. An example of an exponentially stabilizable and exponentially detectable infinite-dimensional system is also considered in this paper. This example shows that the growth bounds of the Toeplitz approximants, as the length of the string increases, and the growth bound of the corresponding infinite-dimensional model, can be significantly different. On the positive side, we give sufficient conditions for the convergence of the growth bounds.