Performance improvement of variable structure filter using discrete reaching condition

The stability of the variable structure filter based on traditional reaching condition was proved but the correct gain which guaranteed a certain convergence rate was not derived. The discrete linear reaching condition and discrete integral reaching condition were introduced to guarantee the convergence rate. Because variable structure filter is based on the system model, system noises cause steady state estimation errors. The discrete integral reaching condition eliminated the steady state errors. Measurement noises have a bad influence on the performance of variable structure filter. Average filtering method and discrete linear reaching condition were combined to derive the correct gain which reduced the influence of measurement noises. The improved variable structure filters are applied to a linear system which contains system noises and measurement noises. Simulation results show that the performance of the variable structure filter is improved.