Minimum entropy and risk-sensitive control: the continuous time case

The relationship between risk-sensitive stochastic control and maximum-entropy H_∞ control was established in the discrete-time case by K. Glover and J.C. Doyle (1988). Analogous calculations are presented here for the continuous time case when certain results on the asymptotic behavior of Toeplitz operators, including convergence rates, can be exploited. The analysis then gives a complete equivalence between the optimal linear steady-state controllers for both problems with the analysis valid for a wide range of infinite-dimensional systems. A state-space approach to this equivalance is presented using techniques similar to those of D.H. Jacobson (1973)