Multi-models in control. Advanced tools for analysis and synthesis (Q2898734)

Due to the fact that a linear approximation of a nonlinear system can be thought as being accurate only as a local description of the system, much work has been devoted in recent years to a more comprehensive approach based on the use of multiple LTI (linear time-invariant) models around various operating points. This multiple models approach is based on the partitioning of the operating range of a system into separate regions and on using local linear models for each region. This yields a convex polytopic representation which can be obtained either directly from the nonlinear model, through the use of certain transformation, either via linearization. Each local model (submodel) is defined as a LTI dynamic system defined for a specific operating point.NEWLINENEWLINEThis book is focused on the analysis and synthesis of control laws for nonlinear systems described by multiple models, the main tools used being Lyapunov's second method and LMI (linear matrix inequalities) formalism. Both quadratic and non-quadratic Lyapunov functionals are being considered, the latter allowing the treatment of multiple models with uncertainties and unknown inputs. Of concern are solely continuous time systems, different types of control laws (state feedback, output feedback) and observers (linear observer, unknown input observers) being studied while taking into account uncertainties.NEWLINENEWLINEThis book consists of five chapters. Chapter 1 represents a primer of the multiple model approach and of LMI formalism. Chapter 2 is concerned with the stability of multiple models, sufficient stability conditions for multiple models with parametric uncertainties being obtained through the use of quadratic and non-quadratic Lyapunov functionals. Chapter 3 treats the synthesis of observers and state estimation for systems with unknown entries and uncertainties. Chapters 4 and 5 are concerned with stabilization by state feedback and with stabilization by output feedback. The synthesis of robust control laws is also treated, two types of uncertainties being considered, namely parametric uncertainties and uncertainties as intervals. The Appendixes are concerned with LMI regions, properties of \(M\)-matrices and comparison principles, respectively.