Continuous-Time Quadratic Guaranteed Cost Filtering

Abstract

Underlying each of the robust filtering algorithms presented in this book is a corresponding class of uncertain systems and filtering performance objective. A common class of uncertain systems in the robust control literature involves a linear time invariant system with a norm bounded uncertainty matrix. For such a class of uncertain systems, the robust control problem that is considered is the quadratic stabilizability problem. This problem involves finding a suitable state feedback controller so that the resulting closed loop system is stable with a single quadratic Lyapunov function. Further details on the quadratic stabilizability problem can be found in the references [12,26,68,75,96,98]. An important approach to the quadratic stabilization problem is the approach based on the algebraic Riccati equation. This approach was developed in [68,96,98]. Also, a connection has emerged between this Riccati equation approach to the quadratic stabilization problem and H ^∞ control theory; e.g., see [68]. This enables results on H ^∞ control such as in [41,94,97] to be applied to problems of robust stabilization.