• 대한전기학회논문지:전력기술부문A
• /
• 제48권5호
• /
• pp.560-570
• /
• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
• /
• pp.1477-1480
• /
• 1997

This paper is concerned with the design of a suboptimal robust Kalman filter using LMI approach for system models in the state space, which are subjected to parameter uncertainties in both the state and measurement atrices. Under the assumption that augmented system composed of the uncertain system and the state estimation error dynamics should be stable, a Lyapunov inequality is obtained. And from this inequaltiy, the filter design problem can be transformed to the gneric LMI problems i.e., linear objective minimization problem and generalized eigenvalue minimization problem. When applied to uncertain linear system modles, the proposed filter can provide the minimum upper bound of the estimation error variance for all admissible parameter uncertainties.

• Transactions on Control, Automation and Systems Engineering
• /
• 제1권2호
• /
• pp.134-140
• /
• 1999

The robust generalized H2 filtering problem for a class of discrete time uncertain linear systems satisfying the sum quadratic constraints(SQCs) is considered. The objective of this paper is to develop robust stability condition using SQCs and design a robust generalized Ha filter to take place of the existing robust Kalman filter. The robust generalized H2 filter is designed based on newly derived robust stability condition. The robust generalized Ha filter bounds the energy to peak gain from the energy bounded exogenous disturbances to the estimation errors under the given positive scalar ${\gamma}$. Unlike the robust Lalman filter, it does not require any spectral assumptions about the exogenous disturbances . Therefore the robust generalized H2 filter can be considered as a deterministic formulation of the robust Kalman filter. Moreover, the variance of the estimation error obtained by the proposed filter is lower than that by the existing robust Kalman filter. The robustness of the robust generalized H2 filter against the uncertainty and the exogenous signal is illustrated by a simple numerical example.

• 대한전기학회논문지:전력기술부문A
• /
• 제48권6호
• /
• pp.735-746
• /
• 1999

We design the robust and inherently fault tolerant decetralized$$H^infty$$ filter for the multisensor state estimation problem when there are insufficient priori informations on the statistical properties of external disturbances. For developing the proposed algorithm, an alternative form of suboptimal$$H^infty$$ filter equations are formulated by applying an alternative form of Kalman filter equations to the indefinite inner product space state model of suboptimal$$H^infty$$ filtering problems. The decentralized$$H^infty$$ filter that consists of local and central fusion filters can be designed effciently using the proposed alternative$$H^infty$$ filiter gain equations. The proposed decentralized$$H^infty$$ filter is robust against un-known external disturbances since it bounds the maximum energy gain from the external disturbances to the estimation errors under the prescribed level$$r^2$$ in both local and central fusion filters and is also fault tolerant due to its inherent redundancy. In addition, the central fusion equations between the global and local data can reduce the unnecessary calculation burden effectively. Computer simulations are made to ceritfy the robustness and fault tolerance of the proposed algorithm.