Robust Control Lyapunov Functions
Significant advances in the theory of linear robust control in recent years have led to powerful new tools for the design and analysis of control systems. A popular paradigm for such theory is depicted in Figure 3.1, which shows the interconnection of three system blocks G, K, and Δ. The plant G relates a control input u and a disturbance input v to a measurement output y and a penalized output z. The control input u is generated from the measured output y by the controller K. All uncertainty is located in the block Δ which generates the disturbance input v from the penalized output z. The plant G, which is assumed to be linear and precisely known, may incorporate some nominal plant as well as frequency-dependent weights on the uncertainty Δ (for this reason G is sometimes called a generalized plant). Once G is determined, the robust stabilization problem is to construct a controller K which guarantees closed-loop stability for all systems Δ belonging to a given family of admissible (possibly nonlinear) uncertain systems.
KeywordsLYAPUNOV Function Robust Stabilization Admissible Control Gain Function Control Constraint
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