Discrete-time ℋ2 and ℋ∞ poly-quadratic filter designs for polytopic LPV systems

This paper addresses novel discrete-time $ \mathcal {H}_2 $ H2 and $ \mathcal {H}_\infty $ H∞ filter designs for polytopic linear parameter-varying (LPV) systems. A less conservative approach is employed to obtain the synthesis conditions, such that the polytopic LPV system state-space representation may have all its matrices subject to time-varying parameters and be solved by an efficient procedure. Parameter-dependent Lyapunov functions are used to derive both $ \mathcal {H}_2 $ H2 and $ \mathcal {H}_\infty $ H∞ discrete-time filter design conditions resulting in a poly-quadratic approach in terms of linear matrix inequalities. A multi-objective $ \mathcal {H}_2/\mathcal {H}_\infty $ H2/H∞ solution is also provided. The proposed conditions have the advantage of recovering the established poly-quadratic concept as a particular case, which was an unresolved problem until the present paper. Moreover, using the addressed approach, it is possible to obtain improved quadratic $ \mathcal {H}_2 $ H2 and $ \mathcal {H}_\infty $ H∞ filters. Numerical examples illustrate the proposed design methods applicability as an observer to estimate LPV system states and its performance in comparison with other approaches.