On some relaxations commonly used in the study of linear systems

Robust vertex‐dependent H∞ and H2 estimation for stochastic linear systems

“…An improved, less conservative, solution compared with the one in our other work was obtained for the H ∞ case in another work of ours by introducing the robust vertex‐dependent approach, which applies the Finsler lemma . Obviously, the quadratic solution is a special case of the latter solution in our other work and it cannot achieve results that are better than the one in the aforementioned work .…”

“…An improved, less conservative, solution compared with the one in our other work 2 was obtained for the H ∞ case in another work of ours 17 by introducing the robust vertex-dependent approach, which applies the Finsler lemma. 18 Obviously, the quadratic solution is a special case of the latter solution in our other work 17 and it cannot achieve results that are better than the one in the aforementioned work. 17 A careful inspection of the solution in our other work, 17 brought in Section 4, reveals that although this solution applies different Lyapunov functions to each vertex of the polytopic uncertainty, it still holds one additional component of the Lyapunov function that is constant over the whole uncertainty polytope.…”

Vertex‐dependent filtering of retarded uncertain state‐multiplicative noisy systems

“…In this work, we address the problems of H ∞ and H 2 robust filtering of linear, uncertain, discrete‐time, retarded, stochastic state‐multiplicative systems. Considering a polytopic‐type uncertain system, we derive a vertex‐dependant solution to the two said problems that is based on the application of a modified Finsler lemma 1 to the solution of the nominal H ∞ case. In our systems, the multiplicative noise appears in the system model in both the delayed and the nondelayed states.…”

Robust stabilization and &#x210B;<inf>&#x221E;</inf> control by means of state-feedback for polytopic linear systems using LMIs and scalar searches

“…Differently from the quadratic stabilization, this approach separates the dynamic matrix of the system from the Lyapunov matrix, allowing the robust gain to be synthesized from the slack variable [10]. Distinct techniques were explored in this context, as for instance the Projection lemma [11][12][13][14] and the Finsler's lemma [15,16]. Other extensively used technique was the introduction of a scalar parameter that, if fixed, still results in LMI conditions [17][18][19][20].…”