The optimal H2 controller for generalized discrete-time systems

Improved robust filter synthesis combining linear matrix inequalities and heuristic algorithms

“…A Lyapunov function V(x(t)) = x(t) T P(𝛼)x(t), with P(𝛼) given in (11), can be used to achieve the augmented system (5) stability. In order to incorporate the additional requirements presented in (15), -procedure 15 can be used, leading to the following conditions…”

“…Filtering problems usually involve uncertainties and additional performance indexes, such as the $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ norms. Recent works exploring $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ guaranteed costs for filtering and fault detection can be mentioned, 7‐10 as well as control problems 11‐13 . The solution of $$$ {\mathscr{H}}_2 $$$ and $$$ {\mathscr{H}}_{\infty } $$$ problems are often initially modeled as a set of bilinear matrix inequalities (BMIs), which are NP‐hard and, thus, difficult to solve 14 .…”

“…Recent works exploring  2 and  ∞ guaranteed costs for filtering and fault detection can be mentioned, [7][8][9][10] as well as control problems. [11][12][13] The solution of  2 and  ∞ problems are often initially modeled as a set of bilinear matrix inequalities (BMIs), which are NP-hard and, thus, difficult to solve. 14 Convexification procedures are applied to these problems to define the conditions as linear matrix inequalities (LMIs), resulting in a synthesis technique based on convex optimization.…”

Optimal Controller Design for Ultra-Precision Fast-Actuation Cutting Systems

“…The controller output u is also included in the cost function to be constrained, because there are hardware limits on the maximum controller output. The optimal control calculation is equivalent to solving a Riccati equation [19], and finally a controller transfer matrix K is calculated.…”