Optimal stabilizing controllers for linear discrete‐time stochastic systems

Abstract

AbstractThe following summarizes the corrections on the online version of the paper, which will be incorporated in the print publication. Section 3. Spectral radius, decay rate and optimal controllers. Theorem 1: The statement ‘For system (1), ρ(MA,C)⩽β∈(0, 1) holds if and only if system (1) has decay rate β−1’ should read as ‘For system (1), if ρ(MA,C)<β∈(0, 1) holds, then system (1) has decay rate β−1. Moreover, if β−1 is a decay rate, then ρ(MA,C)<β∈(0, 1)’. Section 3. Proof necessity. Line 20: Delete ‘(necessity)’; line 21: ‘ρ(MA,C)⩽β∈(0, 1)’ should read as ‘ρ(MA,C)<β∈(0, 1)’; line 22: ‘small arbitrarily ε0>0’ should read as ‘sufficiently small ε0<0’. Sixth page. Line 5: ‘the necessity’ should read as ‘the first part of Theorem 1’; line 7: ‘Sufficiency: Notice’ should read as ‘For the second part, notice’; line 8: ‘decay rate β’ should read as ‘decay rate β−1’; line 11: ‘To prove sufficiency we only need’ should read as ‘We only need’. Seventh page. Corollary 3: The statement ‘For system (5), ρ(M)⩽β∈(0, 1) holds if and only if system …’ should read as ‘For system (5), if ρ(M)<β∈(0, 1) holds, then system …’ Seventh page. Line 14, and eighth page, line 20: ‘decay rate β−1∈(0, 1)’ should read as ‘decay rate β−1’. Seventh page. Line 17, and eighth page, line 23, ‘⩽’ should be ‘<’.