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Over the last several years, researchers have shown that when it is assumed a priori that a fixed-order optimal compensator is minimal, the necessary conditions can be characterized in terms of coupled Riccati and Lyapunov equations, usually termed "optimal projection equations." When the optimal projection equations for H2 optimal control are specialised to full-order control, the standard...
For linear time-invariant systems it has been shown that the solutions to the optimal reduced-order modeling, estimation, and control problems can be characterized using optimal projection equations, sets of Riecati and Lyapunov equations coupled by terms containing a projection matrix. These equations provide a strong theoretical connection between standard full-order results such as linear-quadratic...
The minimal dimension of a linear-quadratic-gaussian (LQG) compensator is usually equal to the dimension of the design plant. This deficiency can lead to implementation problems when considering control-design for high-order systems such as flexible structures and has led to the development of methodologies for the design of optimal (or near optimal) controllers whose dimension is less than that of...
This paper addresses the robest stability and performance analysis problem using a fixed structure approach of the structured singular value. Specifically, using recent results on H2 / H??, a Riccati equation approach is formulated for complex-?? with constant D-scales along with an H2 performance bound. An optimization procedure is proposed in computing optimal D-scales with respect to the H2 performance...
This paper analyses the stability robustness of a Maximum Entropy controller designed for a benchmark problem. Four robustness tests are used: small gain analysis, circle analysis, positive real analysis, and Popov analysis, each of which is guaranteed to give a less conservative result than the previous test. The analysis here is performed graphically although recent research has developed equivalent...
Majorant bounding techniques which appear in the work of Dahlquist and several researchers in large-scale systems analysis have recently been applied to develop robust stability and performance results for linear time-invariant systems with structured uncertainty. Previous results in majorant robustness analysis allow the performance to be measured in terms of the steady state variances of selected...
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