Haar Transform Approximations of Parameter-Dependent Lyapunov and Riccati Equations Matrix Sign-Based Solutions

This paper deals with Lyapunov and Riccati equations for parameter-dependent systems. Such equations arise naturally in analysis, control and model reduction methods for parametric models. The new proposed techniques hinge upon two seminal tools: -The matrix sign function best rational approximation. -The Haar wavelet transform theory. The approximations of parameter-dependent Lyapunov and Riccati equations solutions are didactically presented. Original and significant norm bounds on the computation errors estimates are presented in the context of matrix sign-based solutions. Some examples are given to corroborate the validity of the proposed results.

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