A finite frequency approach to filter design for uncertain discrete‐time systems

Abstract

This paper studies the problem of finite frequency filter design for linear time-invariant discrete-time systems with polytopic uncertainties. Generalized Kalman-Yakubovich-Popov lemma is exploited to formulate the filter design problem in finite frequency domain. A design method is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.

Homogenous polynomial H∞ filtering for uncertain discrete‐time systems: A descriptor approach

“…For uncertainty sets in the first part and in the second one of this example, the performance of the proposed method is clearly better than that of other works 11,12,40,47 in Table 4 and of other works 10,37,41,45 in Table 5, respectively. For uncertainty sets in the first part and in the second one of this example, the performance of the proposed method is clearly better than that of other works 11,12,40,47 in Table 4 and of other works 10,37,41,45 in Table 5, respectively.…”

“…Remark 8. For uncertainty sets in the first part and in the second one of this example, the performance of the proposed method is clearly better than that of other works 11,12,40,47 in Table 4 and of other works 10,37,41,45 in Table 5, respectively. As shown, the importance of the uncertainty range bounds influence performance optimization, as shown via these Tables.…”

Robust finite‐frequency filter design for linear uncertain systems using polynomially parameter‐dependent approach

“…In this section, we will develop a solution to the robust FF filtering problem by the aid of Lemma 2 and HPPD technique, which improves the existing results in the literature (e.g. [25, 33–35]).…”

An improved finite frequency approach to robust filter design for LTI systems with polytopic uncertainties

“…Therefore, in this case, we can eliminate condition . Then, carrying out simple block‐row‐column exchanges, that is, performing a congruence transformation to by Theorem in is reached. Unlike the comparison of our Theorem with Theorem in , it may be difficult to rigorously compare the inclusion relation between our Theorem and Theorem , Corollaries 1, 2 in . But later, we will use an example (see Example ) to show that Theorem can produce less conservative results in comparison with those in for certain systems.…”

“…Unlike the comparison of our Theorem with Theorem in , it may be difficult to rigorously compare the inclusion relation between our Theorem and Theorem , Corollaries 1, 2 in . But later, we will use an example (see Example ) to show that Theorem can produce less conservative results in comparison with those in for certain systems.…”