{"corpus_id":121960136,"paper_sha":"4ec0f12fc619ee605ec3a6125a7b4612d758d625","doi":"10.1109/9.29425","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2042106612,"dblp_id":null,"acl_id":null,"title":"State-space solutions to standard H/sub 2/ and H/sub infinity / control problems","year":1989,"publication_date":"1989-08-01","venue":"","journal":{"name":"IEEE Transactions on Automatic Control","pages":"831-847","volume":"34"},"journal_issn":null,"journal_title":null,"publication_types":["Review"],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Engineering"],"reference_count":28,"citation_count":5066,"influential_citation_count":31,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel.< <ETX xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">&gt;</ETX>","claims":[{"public_id":"cl_3db7de9abc8496e1610eb71f032baa91","status":"active","text":"A controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than γ².","confidence":0.99,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_3db7de9abc8496e1610eb71f032baa91"},{"public_id":"cl_2bff118f354d9532dc91307926e411e4","status":"active","text":"A standard H2 solution is developed in parallel with the H∞ result.","confidence":0.9,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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