Observer-based H<inf>&#x221E;</inf> control using the incremental gain for one-sided Lipschitz nonlinear systems

Abstract

In this paper, an H∞ output feedback controller is presented for one-sided Lipschitz systems, which consists of a state feedback control together with a nonlinear observer. By proposing the L2 incremental gain as an alternative H∞ performance measure to the usual gain, we develop a design technique that guarantees an asymptotically stable closedloop system in the absence of disturbance inputs and further minimizes the incremental gain from disturbances to the controlled output. This method is based on the Lyapunov function parametrization and is formulated in terms of linear matrix inequalities (LMIs). Our result is then validated via numerical example of a discontinuous plant exposed to disturbance inputs with numerous variations.

Attitude stabilization of a rigid spacecraft based on MRPs with unknown bounded time-delay

“…In the problem of time delay control, the spacecraft attitude orientation is most commonly represented with MRPs, for the convenience that time delay could not appear in the nonlinear term, the normalization constrain associated with the quaternions can also be eliminated [8] .…”

A note on observers design for one-sided Lipschitz nonlinear systems

“…For more specialized work, which consist of results on observers for sampled-data nonlinear systems [10], discrete-time sliding mode observers [12], discrete-time nonlinear systems [13], observers for Lipschitz nonlinear systems [8,13,14,16], and Lipschitz nonlinear discrete-time systems with time-delay [15]. Observer design for nonlinear systems with unknown inputs [17][18][19][20], switching nonlinear systems [21], one-sided Lipschitz nonlinear systems [22,23], and so on.…”

Improved exponential observer design for one‐sided Lipschitz nonlinear systems

“…Simulation results on a numerical example are given to illustrate the advantages and effectiveness of the proposed design scheme. IMPROVED EXPONENTIAL NONLINEAR OBSERVER DESIGN 3959 to conservativeness [21][22][23][24][25][26][27][28]. Hu [21,22] first considered the observer design problem for onesided Lipschitz nonlinear systems.…”

“…However, it should be emphasized that Hu [21] actually introduced a modified one-sided Lipschitz condition in which the nonlinearity is scaled via a fixed symmetric definite matrix P (see Definition 1, i.e., P -one-sided Lipschitz condition). As has been pointed out in a recent reference [26], this modification makes the design problem tractable but affects the value of the one-sided Lipschitz constant (i.e., v p strongly depends on P ) and introduces additional constraints on the Lyapunov function. Therefore, observer design for systems with nonlinearities satisfying P -one-sided Lipschitz constraints is still an open problem.More recently, Abbaszadeh and Marquez [27] introduced the standard one-sided Lipschitz condition (Definition 2) and reconsidered the observer design problem.…”

“…Therefore, observer design for systems with nonlinearities satisfying P -one-sided Lipschitz constraints is still an open problem.More recently, Abbaszadeh and Marquez [27] introduced the standard one-sided Lipschitz condition (Definition 2) and reconsidered the observer design problem. To avoid scaling of the one-sided Lipschitz constant, they presented an alternative approach based on a second condition known as the quadratically inner-bounded property and have provided a solution using matrix inequalities [26]. Following this line, further improved results on the design of full-order and reduced-order, unknown input, and exponential observers can be found in [29][30][31].…”