Abstract
A computer-oriented systematic approach to constant-gain filter design for time-invariant linear systems is developed. The trace of the error covariance matrix is minimized subject to constraints on the closed-loop filter eigenvalues. For continuous system representations, the eigenvalues are restricted to a region in the s plane defined by damping ratio and decrement factor inequalities, while discrete representations involve a decrement factor inequality in the z plane. Properties of inner determinants and Lyapunov equations are employed to allow a unified approach to both continuousand discrete-time system representations. The approach is applied to three examples which illustrate filter settling time considerations, transient/steady-state gain tradeoffs, and combined control-estimation possibilities.
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