Guaranteed cost D-stabilization and H∞ D-stabilization for linear discrete time-delay systems

Revisiting the problem of robust H<inf>&#x221E;</inf> control with regional pole location of uncertain discrete-time systems with delayed states

“…Using the change basis matrix given in Proposition 2, it is possible to develop rules for the direct construction of the matrices mentioned in step 2) of section III-A,Ǎ m,d , C m,d , and also the transformed gainsǨ m,τ as function of α, r, and the respective matrices in (1) with (5). As presented in step 2) of section III-A, matrixĎ e,d is already defined, and additionally considering (21) we have matricesB d =B(d, α, r) andB e,d =B e (d, α, r).…”

“…In case of systems with delay in the states, D-stability analysis and H ∞ guaranteed cost characterization cannot be directly applied mainly because of the multiple poles introduced by the delay. Only a few results are available in the literature to characterize the regional pole location [5], [6], [3]. In this note we revisit the problems of robust D(α, r)-stability [5], [7], [8] analysis and synthesis of controller taking into account the minimization of the H ∞ guaranteed cost for the class of linear uncertain time-invariant discrete-time systems with (constant and bounded) uncertain delay in the states.…”

“…Only a few results are available in the literature to characterize the regional pole location [5], [6], [3]. In this note we revisit the problems of robust D(α, r)-stability [5], [7], [8] analysis and synthesis of controller taking into account the minimization of the H ∞ guaranteed cost for the class of linear uncertain time-invariant discrete-time systems with (constant and bounded) uncertain delay in the states. The D(α, r)-stability is investigated here means a disk region with center in (α, 0) and radius r entirely inside the unitary circle centered at the origin of the complex plane where all eigenvalues are inside it.…”

“…Also we avoid the system augmentation to obtain a delay-free system [2] due the known problems in such an approach [?] An alternative approach has been proposed in [7] and has been used in [3], to deal with non-fragile controller design, and in [5]. The improved conditions presented in [5], using the same LyapunovKrasovskii (L-K) function employed here, usually leads to more conservative results compared with ours.…”

Guaranteed cost consensus for multi-agent systems with time delays

“…[20][21][22][23]. Because consensus problems for multi-agent systems focus on state errors among agents and control problems for isolated systems focus on states, these approaches in [20][21][22][23] cannot be directly used to deal with guaranteed cost consensus problems. To the best of our knowledge, there are few literatures to investigate guaranteed cost consensus problems for multi-agent systems.…”