State estimation for linear hybrid systems with periodic jumps and unknown inputs

Abstract

In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger-like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input-to-state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding-mode observer is added to the Luenberger-like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.

Observer design for hybrid dynamical systems with approximately known jump times

“…General hybrid systems are considered in a unified framework, only assuming knowledge about the time between successive jumps, which allows any type of solutions, from Zeno and eventually discrete, to eventually continuous trajectories; 2. Preliminary results were given in [10,41], but restricted to hybrid systems with linear f and g, and when at least either the flow dynamics or the jump dynamics are detectable. Here, more general nonlinear sufficient conditions are obtained, even in the case were neither the continuous nor the discrete dynamics of the plant are detectable, but, the hybrid plant as a whole is; 3.…”

“…with a d < 0 as in [10,41], where τ denotes the rADT or the maximal length of flow. In particular, [10,Example 4.2] shows that it can be done analytically for a bouncing ball exhibiting Zeno trajectories modeled by (3) with λ < 1, and with the output h d (x) = x 1 only available at jumps.…”

Hysteresis-based switching observers for linear systems using quadratic boundedness

“…A hybrid scheme is presented in [9] to design observers with different sets of coordinates with respect to the system to estimate. Hybrid observers with periodic jumps are considered in [29,30]. In [6], the construction of observers with state trajectories permanently remaining in compact convex sets is addressed within a hybrid framework, while ensuring robustness to disturbances.…”

Residual Neural Network-Based Observer Design for Continuous Stirred Tank Reactor Systems

“…The extended state observer (ESO) is a popular observer in the chemical industry nowadays [7,8]. It can estimate the states of a nonlinear system [9], which is different from the Luenberger observer constrained by the linear model [10,11]. However, ESO has some drawbacks such as the inability to track the states of the original system and the requirement of order information [12][13][14].…”