Existence Conditions of H∞ Suboptimal Controllers
The first fundamental issue one faces in an H ∞ optimization problem, is when, or under what conditions a γ suboptimal controller exists. Fortunately, the problem regarding the existence conditions of γ-suboptimal controllers for either the regular or singular type of continuous-time or discrete-time systems has almost been completely solved in the literature. As it was mentioned in the introduction, there were four main different approaches developed in early years, which include: 1) Interpolation approach (see e.g., Limbeer and Anderson ); 2) Frequency domain approach (see e.g., Doyle , Francis  and Glover ); 3) Polynomial approach (see e.g., Kwakernaak ); and 4) J-spectral factorization approach (see e.g., Kimura ). All these techniques mainly deal with the regular problem.
KeywordsRiccati Equation Imaginary Axis Existence Condition Full Column Rank Algebraic Riccati Equation
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