Study on H_2/H_* Optimal Control Using Descriptor Riccati Equation

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This research is concerned with the H_2/H_* optimal control and filtering problems for a descriptor system. The following are the results obtained for the past two years.1. For a discrete-time descriptor system, we have developed a new algorithm for solving the H_2 control problem and a related spectral factorization. We have derived a numerical method for computing optimal controls and spectral factors based on the generalized eigenproblem (GEP) approach.2. Extending the above result, we also developed a (J, J')-spectral factorization algorithm for a discrete-time descriptor system.3. For a continuous-time descriptor system, we have presented a new generalized Riccati equation to solve the LQ regulator problem. A numerical algorithm is also developed based on the GEP.4. We have developed spectral and J-spectral factorization algorithms for a continuous-time descriptor systems.5. Based on the J-spectral factorization and a Youla parametrization for descriptor systems, we have developed a solution method for H_* control for continuous-time descriptor systems. At present, we are still extensively studying H_* control problem along this line.6. Applying model matching technique, the parametrization of all stable unbiased H_* estimators is derived. Also, we have presented a design method of full-order estimator under the weighted H_* error performance. Although the results for H_* estimators are obtained for state-space models, we will be able to extend these results to the H_* estimation for descriptor systems.