Control design for bilinear systems with a guaranteed region of stability: An LMI-based approach

Robust optimal control of bilinear DC–DC converters

“…The polytopic modeling of bilinear terms presented in Tarbouriech, Queinnec, Calliero, and Peres (2009) has been adapted to the converter model in order to cope with the effect of such bilinear terms on the stability of the closed-loop system. With this method, the possible values of the term B nx ðtÞ are included in a convex polytope X ðxÞ:…”

“…During the changes of operating point it is assumed that references and disturbances are equal to zero. The conditions ensuring system stability despite the nonlinear term have been adapted from Tarbouriech et al (2009) in the following proposition:…”

Stability of bilinear sampled-data systems with an emulation of static state feedback

“…In this method, the MASP is calculated by the expression (18), based on L and γ. L is calculated analytically, whereas γ is found by solving LMI conditions. The optimization problem is a minimization of γ ′ because for any constant L, T (·, L) is a strictly decreasing function.…”

“…Consider the example of bilinear systems in [17] and [18], where a continuous-time state feedback controllers has been computed in order to locally stabilize the bilinear system. The system is described by the matrices In [18], the linear state feedback Using Method 1, we found that the system is locally stable ifT < T = 2.7 ms. This was calculated from (18) Using Method 2, we found that the sampled-data system is locally stable for a larger MASPT ≤ T = 12 ms.…”

“…The feedback stabilization of bilinear systems is a challenging problem, and several controller structures may be found in the literature [15], [16]. Recently in [17] and [18], linear matrix inequalities (LMI) have been used to find a linear state feedback controller that ensures the local stability in an ellipsoidal domain. The next phase toward practical applications, is to study the robustness to a sampled-data implementation.…”