Performance Analysis Of Nonlinear Systems Research Articles

Convex incremental dissipativity analysis of nonlinear systems

Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to the regions around the equilibrium points of these nonlinear systems. The incremental framework, based on the convergence of the system trajectories, removes this limitation. We investigate how stability and performance characterizations of nonlinear systems in the incremental framework are linked to dissipativity, and how general performance characterization beyond the L2-gain concept can be understood in this framework. This paper presents a matrix inequalities-based convex incremental dissipativity analysis for nonlinear systems via quadratic storage and supply functions. The proposed dissipativity analysis links the notions of incremental, differential, and general dissipativity. We show that through differential dissipativity, incremental and general dissipativity of the nonlinear system can be guaranteed. These results also lead to the incremental extensions of the L2-gain, the generalized H2-norm, the L∞-gain, and passivity of nonlinear systems.

Robust control of processes subject to saturation nonlinearities

Motivated by current practice, a two-step design technique for saturating systems is studied. First an “optimal” (for example in the H∞ sense) linear controller is designed neglecting saturation. Then a saturation compensation scheme (anti-windup) is designed which provides graceful degradation of closed-loop performance in the face of saturation. The focus in this paper is on the second step, and obtaining general results and insights applicable to any (linear) system subject to saturation. A design technique is developed which results in effective saturation compensation for a given multivariable plant and linear compensation design. For particular controller choices the resulting saturation compensator is shown to be equivalent to proven techniques includin g anti-rest windup and internal model control (IMC). Tools are developed for robust stability and performance analysis of nonlinear systems. Well-known structured singular value robustness tests for linear systems are extended to a class of nonlinear systems. Sufficient conditions are developed which guarantee closed-loop stability for all plants in a structured uncertainty set and for all nonlinearities of a specified form. These tests result in simple conditions on the initial linear controller design which must be satisfied in order to guarantee robust stability of the saturating plant. In some instances this requires that the original linear design be detuned. A procedure for performing this detuning is outlined. A promising single-step procedure for the synthesis of optimal robust linear controllers for saturating systems is also outlined. While this approach lacks the simplicity of the two-level decomposition, it appears to have promise for situations where the impact of the saturation on the closed loop is severe.