Square-root H2 and H∞ synthesis algorithms for sequentially semi-separable systems

We consider the problem of designing H₂ and H_∞ linear estimators for time-varying spatially interconnected systems distributed in one spatial dimension. In general, numerical implementation of the algebraic Riccati equation (ARE) solution for such systems is a complex and computationally expensive operation. However, the spatially interconnected systems can be described by state-space models whose matrices have a special structure, called “sequentially semi-separable” (SSS). Using only efficient and structure-preserving arithmetic operations, the H₂ and H_∞ estimation problems are solved by means of square-root array algorithms. Our solution has thus, linear computational complexity and is a viable approach for large scale systems.