See Appendix. Note that Theorem 1 implies that the network (4) reaches an output agreement providing that there exist constant vectors (x¯, η¯) ∈ (Ωn)N ×(Ωe)M satisfying (6), (7), and thus
See Appendix the vectors and matrices MG, AG, θG, and uG, as MG = diag(Mi), AG = diag(Ai), θG = col(θi), uG = col(ui), and δG = col(δi) where i ∈ VG. The vectors and matrices AI , θI , and uI are defined as AI = diag(Ai), θI = col(θi), uI = col(ui), and δG = col(δi) with i ∈ VI . In addition, let AL = diag(Ai), θL = col(θi) and δL = col(δi) where i ∈ VL. Finally, let P = col(Pi), θ = col(θG, θI, θL), and sin(x) := col(sin(xi)) for a given vector x. Then, it is easy to observe that the dynamics of the synchronous generators, the inverters, and the loads can be written compactly as: MGθ¨G + AGθ˙G = −BGΓsin(B⊤θ) + uG − δG (26a)
See Appendix. Changing Shift Employees changing from one shift to another and commencing work within hours of original starting time, will be paid overtime rates for the first shift at each change. Employees working two (2) shifts or more on a new shift shall be considered transferred. This will not, however, involve the payment of punitive overtime rates to employees changing off where employees work alternately on stated shifts, to employees changing positions under the exercise of their seniority rights, nor to employees in regular relief service.
See Appendix. B" All eligible employees shall, subject to the conditions therein, have the benefit of the various plans for hourly rated employees outlined in Appendix "B".
See Appendix. A" The classifications and wage rates for the effective period of this Agreement shall be those attached hereto in Appendix "A".
See Appendix. Remark 3 Note that in case the controller at a node i ∈ I11 or i ∈ I21 does not have access to the desired output y∗, one can set ui to a constant, namely a nominal value, and incor- porate the node i in the subdynamics of (11) corresponding to the nodes indexed by I12 or I22, respectively. In Theorem 2, the control input u has been designed such that output agreement on a prescribed vector y∗ is achieved for the network. Observe that the “steady-state” control signal u¯ = ξ¯ is primarily determined by the initialization of the system/controller. Next, under the constraint of output agreement (6), we aim to minimize the following quadratic cost function 0 = (J11 − R11)∇H11(x¯11) min = 1 Σ u¯T Q u¯ (16) n − G11(B11 ⊗ I)∇He(η¯) u¯ 2 i∈Ic + G11u¯11 + G11δ11 (13b) n 0 = (J12 − R12)∇H12(x¯12) − G12(B12 ⊗ I)∇He(η¯) + G12δ12 (13c) n 0 = (J21 − R21)∇H21(x¯21) − G21(B21 ⊗ I)∇He(η¯) (13d) + G21u¯21 + G21δ21 n 0 = (J22 − R22)∇H22(x¯22) − G22(B22 ⊗ I)∇He(η¯) + G22δ22 (13e) where Qi ∈ Rm × Rm is a positive definite matrix for each i, and Ic = I11 ∪ I21. Note that the optimization above determines the steady-state distribution of the control effort
See Appendix. 1. In year one of the contract, 2013-2014, the following will apply:
See Appendix. Lab Load - Establishing Eligibility. The Full-time Service Obligation (Load obligation) is thirty (30) teaching units of Calculated A Hours (CAHs) per Academic Year, averaging fifteen (15) Calculated A Hours (CAHs) per Semester, or the equivalent as defined herein.
See Appendix. Every employee, except shall be subject to a probationary period of ninety (90) calendar days of continuous employment commencing on the date of such employment, during which period the Board shall have the right to discharge such employee without grievance, provided that the employee shall have the right to grieve on any other matters coming within the scope of this Agreement, and shall otherwise enjoy the rights, privileges and benefits, and shall conscientiously perform and observe all obligations and responsibilities contained in this Agreement. (revised and renumbered 89) Employees in the rank of Communicator shall be subject to a probationary period of one hundred and twenty (120) calendar days of continuous employment commencing on the date of such employment, during which period the Board shall have the right to discharge such employee without grievance, provided that the employee shall have the right to grieve on any other matters coming within the scope of this Agreement and shall otherwise enjoy the rights, privileges and benefits, and shall conscientiously perform and observe all obligations and responsibilities contained in this Agreement. (new 89) An employee who is appointed or promoted to another position within the jurisdiction of the Board, shall be subject to a probationary period of ninety (90) calendar days of continuous employment, commencing on the date of such appointment or promotion, at the end of which time the Board shall either such employee in the new position or shall return the employee to their former rank or classification without loss of seniority. Other members affected shall be returned to their previous position without loss of seniority. (revised 97)
See Appendix. ARTICLEVIII
