Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in Japa

Group and total dissipativity and stability of multi-equilibria hybrid automata

Complex systems, which consist of different interdependent and interlocking subsystems, typically have multiple equilibrium points associated with different set points of each operation mode. These systems are usually interpreted as switched systems, or in general, as hybrid systems. Surprisingly, the consideration of multiple equilibria is not common in hybrid systems’ literature, being typically focused on the study of stability and dissipativity properties for switched systems whose subsystems share the same equilibrium point. This paper will expand the discussion to the case of having multiple co-existing equilibrium points for hybrid systems modelled as hybrid automata, which are more general than switched systems. A classification of equilibria for hybrid automata is offered, and some stability related properties are shown for them. Moreover, some dissipativity-related properties are studied. The chief idea of our approach is to identify stable and dissipative components as group of discrete locations within the hybrid automaton. Two examples are used to illustrate our conclusions

Passivity analysis and passification of discrete-time hybrid systems

This paper proposes several (sufficient) criteria based on the numerical solution of systems of linear matrix inequalities (LMIs) for proving the passivity of discrete-time hybrid systems in piecewise affine form, and for the synthesis of switched linear control laws that enforce passivity

Passivity analysis and passification of discrete-time hybrid systems

For discrete-time hybrid systems in piecewise affine or piece-wise polynomial (PWP) form, this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or PWP storage functions. By exploiting linear matrix inequality techniques and sum of squares decomposition methods, passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages, providing a tool particularly important for stability of interconnected heterogeneous dynamical systems

Passivity analysis and passification of discrete-time hybrid systems

This paper proposes several (sufficient) criteria based on the numerical solution of systems of linear matrix inequalities (LMIs) for proving the passivity of discrete-time hybrid systems in piecewise affine form, and for the synthesis of switched linear control laws that enforce passivity

Passivity analysis and passification of discrete-time hybrid systems

3noreservedFor discrete-time hybrid systems in piecewise affine or piece- wise polynomial (PWP) form, this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or PWP storage functions. By exploiting linear matrix inequality techniques and sum of squares decomposition methods, passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages, providing a tool particularly important for stabil- ity of interconnected heterogenous dynamical systems.mixedA. BEMPORAD; G. BIANCHINI; F. BROGIBemporad, Alberto; Bianchini, Gianni; Brogi, Filipp