Piecewise linear control systems : a computational approach / Mikael Johansson.

Includes bibliographical references and index (pages [185]-202)

Table Of Contents: Introduction Piecewise Linear Modeling Model Representation Solution Concepts Uncertainty Models Modularity and Interconnections Piecewise Linear Function Representations Comments and References Structural Analysis Equilibrium Points and the Steady-State Characteristic Constraint Verification and Invariance Detecting Attractive Sliding Modes on Cell Boundaries Comments and References Lyapunov Stability Exponential Stability Quadratic Stability Conservatism of Quadratic Stability From Quadratic to Piecewise Quadratic Interlude: Describing Partition Properties Piecewise Quadratic Lyapunov Functions Analysis of Piecewise Linear Differential Inclusions Analysis of Systems with Attractive Sliding Modes Improving Computational Efficiency Piecewise Linear Lyapunov Functions A Unifying View Comments and References Dissipativity Analysis Dissipativity Analysis via Convex Optimization Computation of L2-induced Gain Estimation of Transient Energy Dissipative Systems with Quadratic Supply Rates Comments and References Controller Design Quadratic Stabilization of Piecewise Linear Systems Controller Synthesis based on Piecewise Quadratics Comments and References Selected Topics Estimation of Regions of Attraction Rigorous Analysis of Smooth Nonlinear Systems Automated Partition Refinements Fuzzy Logic Systems Comments and References Linear Hybrid Dynamical Systems Linear Hybrid Dynamical Systems Analysis using Discontinuous Lyapunov Functions Stability Analysis using Lyapunov Functionals Comments and References Concluding Remarks A. Computational Issues Linear and Semidefinite Programming Polyhedra, Polytopes, and Ellipsoids Polyhedral Partitions Constraint Matrices On the S-procedure in Piecewise Quadratic Analysis Comments and References B. Proofs Proofs from Chapter 2 Proofs from Chapter 4 Proofs from Chapter 5 Proofs from Chapter 6 Proofs from Chapter 7 Proofs from Chapter A C. Bibliography